http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2013 , Hindawi Publishing Corporation . All rights reserved. Tue, 26 Mar 2013 18:39:59 +0000 http://www.hindawi.com/isrn/geometry/2013/932564/ The object of the present paper is to study some curvature conditions on -contact metric manifolds. R. N. Singh and Shravan K. Pandey Copyright © 2013 R. N. Singh and Shravan K. Pandey. All rights reserved. Thu, 07 Mar 2013 09:50:34 +0000 http://www.hindawi.com/isrn/geometry/2013/412593/ We study and obtain results on Ricci solitons in Kenmotsu manifolds satisfying , , , and , where and are C-Bochner and pseudo-projective curvature tensor. C. S. Bagewadi, Gurupadavva Ingalahalli, and S. R. Ashoka Copyright © 2013 C. S. Bagewadi et al. All rights reserved. Tue, 26 Feb 2013 08:03:12 +0000 http://www.hindawi.com/isrn/geometry/2013/787014/ We introduce the different notions of a new class of continuous functions called generalized semi Lambda (gs) continuous function in topological spaces. Its properties and characterization are also discussed. S. Pious Missier and Vijilius Helena Raj Copyright © 2013 S. Pious Missier and Vijilius Helena Raj. All rights reserved. Wed, 30 Jan 2013 16:49:06 +0000 http://www.hindawi.com/isrn/geometry/2013/927159/ This paper deals with the classification of a 3-dimensional almost Kenmotsu manifold satisfying certain geometric conditions. Moreover, by applying our main classification theorem, we obtain some suffcient conditions for an almost Kenmotsu manifold of dimension 3 to be an Einstein-Weyl manifold. Yaning Wang and Ximin Liu Copyright © 2013 Yaning Wang and Ximin Liu. All rights reserved. Thu, 27 Dec 2012 16:01:37 +0000 http://www.hindawi.com/isrn/geometry/2012/309486/ The purpose of the present paper is to characterize pseudoprojectively flat and pseudoprojective semisymmetric generalized Sasakian-space-forms. H. G. Nagaraja, G. Somashekhara, and Savithri Shashidhar Copyright © 2012 H. G. Nagaraja et al. All rights reserved. Tue, 25 Dec 2012 15:29:11 +0000 http://www.hindawi.com/isrn/geometry/2012/876276/ The object of the present paper is to characterize generalized Sasakian-space-forms satisfying certain curvature conditions on conharmonic curvature tensor. In this paper we study conharmonically semisymmetric, conharmonically flat, -conharmonically flat, and conharmonically recurrent generalized Sasakian-space-forms. Also generalized Sasakian-space-forms satisfying and have been studied. U. C. De, R. N. Singh, and Shravan K. Pandey Copyright © 2012 U. C. De et al. All rights reserved. Tue, 11 Dec 2012 09:46:06 +0000 http://www.hindawi.com/isrn/geometry/2012/680247/ There are 106 individual types of singular points for reducible complex sextic curves. David A. Weinberg and Nicholas J. Willis Copyright © 2012 David A. Weinberg and Nicholas J. Willis. All rights reserved. Mon, 03 Dec 2012 12:57:40 +0000 http://www.hindawi.com/isrn/geometry/2012/659430/ The object of the present paper is to study a quarter-symmetric nonmetric connection on a -Sasakian manifold. In this paper we consider the concircular curvature tensor and conformal curvature tensor on a -Sasakian manifold with respect to the quarter-symmetric nonmetric connection. Next we consider second-order parallel tensor with respect to the quarter-symmetric non-metric connection. Finally we consider submanifolds of an almost paracontact manifold with respect to a quarter-symmetric non-metric connection. Abul Kalam Mondal and U. C. De Copyright © 2012 Abul Kalam Mondal and U. C. De. All rights reserved. Wed, 28 Nov 2012 08:10:51 +0000 http://www.hindawi.com/isrn/geometry/2012/309145/ We study submersion of CR-submanifolds of an l.c.q.K. manifold. We have shown that if an almost Hermitian manifold admits a Riemannian submersion of a CR-submanifold of a locally conformal quaternion Kaehler manifold , then is a locally conformal quaternion Kaehler manifold. Majid Ali Choudhary, Mahmood Jaafari Matehkolaee, and Mohd. Jamali Copyright © 2012 Majid Ali Choudhary et al. All rights reserved. Wed, 14 Nov 2012 10:00:27 +0000 http://www.hindawi.com/isrn/geometry/2012/804520/ The aim of the present paper is to study geodesic contact screen Cauchy Riemannian (SCR-) lightlike submanifolds, geodesic screen transversal lightlike, and geodesic transversal lightlike submanifolds of indefinite Kenmotsu manifolds. S. M. Khursheed Haider, Mamta Thakur, and Advin Copyright © 2012 S. M. Khursheed Haider et al. All rights reserved. Mon, 05 Nov 2012 16:12:53 +0000 http://www.hindawi.com/isrn/geometry/2012/970682/ We study curvature properties in -contact metric manifolds. We give the characterization of -Einstein -contact metric manifolds with associated scalars. H. G. Nagaraja and C. R. Premalatha Copyright © 2012 H. G. Nagaraja and C. R. Premalatha. All rights reserved. Thu, 13 Sep 2012 15:11:47 +0000 http://www.hindawi.com/isrn/geometry/2012/251213/ We introduce and study hemi-slant lightlike submanifolds of an indefinite Kenmotsu manifold. We give an example of hemi-slant lightlike submanifold and establish two characterization theorems for the existence of such submanifolds. We prove some theorems which ensure the existence of minimal hemi-slant lightlike submanifolds and obtain a condition under which the induced connection ∇ on M is a metric connection. An example of proper minimal hemi-slant lightlike submanifolds is also given. S. M. Khursheed Haider, Mamta Thakur, and Advin Copyright © 2012 S. M. Khursheed Haider et al. All rights reserved. Thu, 06 Sep 2012 13:26:43 +0000 http://www.hindawi.com/isrn/geometry/2012/591296/ We study some 𝐿𝑘-finite-type Euclidean hypersurfaces. We classify 𝐿𝑘-1-type Euclidean hypersurfaces and 𝐿𝑘-null-2-type Euclidean hypersurfaces with at most two distinct principal curvatures. We also prove that, under some mild restrictions, there exists no 𝐿𝑘-null-3-type Euclidean hypersurface. Akram Mohammadpouri and S. M. B. Kashani Copyright © 2012 Akram Mohammadpouri and S. M. B. Kashani. All rights reserved. Thu, 16 Aug 2012 14:03:01 +0000 http://www.hindawi.com/isrn/geometry/2012/165808/ In this note we study the growth of the number of periodic points for non-degenerate actions of commuting hyperbolic toral automorophisms. Mark Pollicott Copyright © 2012 Mark Pollicott. All rights reserved. Wed, 08 Aug 2012 09:22:46 +0000 http://www.hindawi.com/isrn/geometry/2012/421384/ We study Ricci solitons in 𝛼-Sasakian manifolds. It is shown that a symmetric parallel second order-covariant tensor in a 𝛼-Sasakian manifold is a constant multiple of the metric tensor. Using this, it is shown that if ℒ𝑉𝑔+2𝑆 is parallel where 𝑉 is a given vector field, then (𝑔,𝑉,𝜆) is Ricci soliton. Further, by virtue of this result, Ricci solitons for 𝑛-dimensional 𝛼-Sasakian manifolds are obtained. Next, Ricci solitons for 3-dimensional 𝛼-Sasakian manifolds are discussed with an example. Gurupadavva Ingalahalli and C. S. Bagewadi Copyright © 2012 Gurupadavva Ingalahalli and C. S. Bagewadi. All rights reserved. Wed, 08 Aug 2012 09:21:36 +0000 http://www.hindawi.com/isrn/geometry/2012/685103/ Given 𝒫 a fundamental polyhedron for the action of 𝐺, a classical kleinian group, acting in 𝑛-dimensional hyperbolic space, and Γ, a finite index subgroup of 𝐺, one obtains a fundamental domain for Γ pasting copies of 𝒫 by a Schreier process. It also generalizes the side pairing generating theorem for exact or inexact polyhedra. It is proved as well that the general Möbius group acting in ℝ𝑛 is transitive on “𝑘-spheres”. Hence, describing the hyperbolic 𝑘-planes in the upper half space model intrinsically, and providing also an alternative proof of the transitive action on them. Some examples are given in detail, derived from the classical modular group and the Picard group. Antonio Lascurain Orive and Rubén Molina Hernández Copyright © 2012 Antonio Lascurain Orive and Rubén Molina Hernández. All rights reserved. Mon, 09 Jul 2012 14:57:49 +0000 http://www.hindawi.com/isrn/geometry/2012/560760/ The main purpose of this paper is to illustrate the mutual benefit to combinatorics and geometry by considering a topic from both sides. Al-Azemi and Betten enumerate the distinct combinatorial (223) configurations that are triangle free. They find a very large number of such configurations, but when taking into account the automorphism group of each, they find two cases in which there is only a single configuration. On the heuristic assumption that an object that is unique in some sense may well have other interesting properties, the geometric counterparts of these configurations were studied. Several unexpected results and problems were encountered. One is that the combinatorially unique (223) configuration with automorphisms group of order 22 has three distinct geometric realizations by astral configurations. Branko Grünbaum Copyright © 2012 Branko Grünbaum. All rights reserved. Sun, 10 Jun 2012 14:12:56 +0000 http://www.hindawi.com/isrn/geometry/2012/254235/ We develop the theory of poset pinball, a combinatorial game introduced by Harada-Tymoczko to study the equivariant cohomology ring of a GKM-compatible subspace 𝑋 of a GKM space; Harada and Tymoczko also prove that, in certain circumstances, a successful outcome of Betti poset pinball yields a module basis for the equivariant cohomology ring of 𝑋. First we define the dimension pair algorithm, which yields a successful outcome of Betti poset pinball for any type 𝐴 regular nilpotent Hessenberg and any type 𝐴 nilpotent Springer variety, considered as GKM-compatible subspaces of the flag variety. The algorithm is motivated by a correspondence between Hessenberg affine cells and certain Schubert polynomials which we learned from Insko. Second, in a special case of regular nilpotent Hessenberg varieties, we prove that our pinball outcome is poset-upper-triangular, and hence the corresponding classes form a 𝐻∗𝑆1(pt)-module basis for the S1-equivariant cohomology ring of the Hessenberg variety. Darius Bayegan and Megumi Harada Copyright © 2012 Darius Bayegan and Megumi Harada. All rights reserved. Tue, 24 Apr 2012 15:03:30 +0000 http://www.hindawi.com/isrn/geometry/2012/367467/ We study (a) the class of 3-dimensional pseudosymmetric contact metric manifolds with harmonic curvature and 𝑇𝑟𝑙 constant along the direction of 𝜉 and (b) the class of (𝜅,𝜇,𝜈)-contact metric pseudosymmetric 3-manifolds of type constant in the direction of 𝜉. Evaggelia Moutafi Copyright © 2012 Evaggelia Moutafi. All rights reserved. Tue, 24 Apr 2012 13:07:32 +0000 http://www.hindawi.com/isrn/geometry/2012/682829/ We define 𝜃-ℐ𝑔-Closed sets and discuss their properties. Using these sets, we characterize 𝒯1/2-𝑠𝑝𝑎𝑐𝑒𝑠 and 𝒯ℐ-𝑆𝑝𝑎𝑐𝑒𝑠. M. Navaneethakrishnan and S. Alwarsamy Copyright © 2012 M. Navaneethakrishnan and S. Alwarsamy. All rights reserved. Tue, 10 Apr 2012 15:30:59 +0000 http://www.hindawi.com/isrn/geometry/2011/812541/ In Ricci flow theory, the topology of Ricci soliton is important. We call a metric quasi-Einstein if the m-Bakry-Emery Ricci tensor is a constant multiple of the metric tensor. This is a generalization of gradient shrinking Ricci soliton. In this paper, we will prove the finiteness of the fundamental group of m-quasi-Einstein with a positive constant multiple. Hee Kwon Lee Copyright © 2011 Hee Kwon Lee. All rights reserved. Sun, 08 Apr 2012 13:42:15 +0000 http://www.hindawi.com/isrn/geometry/2012/804051/ The algebraic methods are used in the web geometry, in particular in the 3-web. Along the line, we suggest a new, alternative algebraic method for computation of the quantities 1∇𝑙𝑎𝑖𝑗𝑘, 2∇𝑙𝑎𝑖𝑗𝑘, and 𝑑𝑖𝑗𝑘𝑙𝑚 by means of the embedding of local loops into Lie groups. Thomas B. Bouetou Copyright © 2012 Thomas B. Bouetou. All rights reserved. Thu, 05 Apr 2012 09:41:56 +0000 http://www.hindawi.com/isrn/geometry/2012/348618/ A remarkably simple Diophantine quadratic equation is known to generate all, Apollonian integral gaskets (disk packings). A new derivation of this formula is presented here based on inversive geometry. Also, occurrence of Pythagorean triples in such gaskets is discussed. Jerzy Kocik Copyright © 2012 Jerzy Kocik. All rights reserved. Tue, 27 Mar 2012 10:38:42 +0000 http://www.hindawi.com/isrn/geometry/2012/983403/ This is a review paper of the essential research on metric (Killing, homothetic, and conformal) symmetries of Riemannian, semi-Riemannian, and lightlike manifolds. We focus on the main characterization theorems and exhibit the state of art as it now stands. A sketch of the proofs of the most important results is presented together with sufficient references for related results. K. L. Duggal Copyright © 2012 K. L. Duggal. All rights reserved. Mon, 26 Mar 2012 10:43:37 +0000 http://www.hindawi.com/isrn/geometry/2012/484312/ We consider the spherical boundary, a conformal boundary using a special class of conformal distortions. We prove that certain bounds on volume growth of suitable metric measure spaces imply that the spherical boundary is “small” (in cardinality or dimension) and give examples to show that the reverse implications fail. We also show that the spherical boundary of an annular convex proper length space consists of a single point. This result applies to 𝑙2-products of length spaces, since we prove that a natural metric, generalizing such “norm-like” product metrics on a (possibly infinite) product of unbounded length spaces, is annular convex. Stephen M. Buckley and Simon L. Kokkendorff Copyright © 2012 Stephen M. Buckley and Simon L. Kokkendorff. All rights reserved. Sun, 18 Mar 2012 14:36:15 +0000 http://www.hindawi.com/isrn/geometry/2012/126358/ We show a new method to construct constant slope surfaces with quaternions. Moreover, we give some results and illustrate an interesting shape of constant slope surfaces by using Mathematica. Murat Babaarslan and Yusuf Yayli Copyright © 2012 Murat Babaarslan and Yusuf Yayli. All rights reserved. Thu, 08 Mar 2012 14:54:42 +0000 http://www.hindawi.com/isrn/geometry/2012/535101/ In this paper it is shown that a 2𝑛-dimensional almost symplectic manifold (𝑀,𝜔) can be endowed with an almost paracomplex structure 𝐾, 𝐾2=Id𝑇𝑀, and an almost complex structure 𝐽, 𝐽2=−Id𝑇𝑀, satisfying 𝜔(𝐽𝑋,𝐽𝑌)=𝜔(𝑋,𝑌)=−𝜔(𝐾𝑋,𝐾𝑌) for 𝑋,𝑌∈𝑇𝑀, 𝜔(𝑋,𝐽𝑋)>0 for 𝑋≠0 and 𝐾𝐽=−𝐽𝐾, if and only if the structure group of 𝑇𝑀 can be reduced from 𝑆𝑝(2𝑛) (or 𝑈(𝑛)) to 𝑂(𝑛). In the symplectic case such a manifold (𝑀,𝜔,𝐽,𝐾) is called an almost hyper-para-Kähler manifold. Topological and metric properties of almost hyper-para-Kähler manifolds as well as integrability of (𝐽,𝐾) are discussed. It is especially shown that the Pontrjagin classes of the eigenbundles 𝑃± of 𝐾 to the eigenvalues ±1 depend only on the symplectic structure and not on the choice of 𝐾. Jochen Merker Copyright © 2012 Jochen Merker. All rights reserved. Mon, 05 Mar 2012 13:56:17 +0000 http://www.hindawi.com/isrn/geometry/2012/709243/ The paper deals with the study on conservative C-Bochner curvature tensor in K-contact and Kenmotsu manifolds admitting semisymmetric metric connection, and it is shown that these manifolds are η-Einstein with respect to Levi-Civita connection, and the results are illustrated with examples. Gurupadavva Ingalahalli and C. S. Bagewadi Copyright © 2012 Gurupadavva Ingalahalli and C. S. Bagewadi. All rights reserved. Sun, 04 Mar 2012 09:47:19 +0000 http://www.hindawi.com/isrn/geometry/2012/359403/ The purpose of this paper is to extend the concept of homotopy extension property in homotopy theory for topological spaces to its analogical structure in homotopy theory for topological semigroups. In this extension, we also give some results concerning on absolutely retract and its properties. Adem Kılıçman and Amin Saif Copyright © 2012 Adem Kılıçman and Amin Saif. All rights reserved. Wed, 29 Feb 2012 13:10:16 +0000 http://www.hindawi.com/isrn/geometry/2012/757489/ We classify isometries of the real hyperbolic 4-space by their conjugacy classes of centralizers. We use the representation of the isometries by 2×2 quaternionic matrices to obtain this characterization. Another characterization in terms of conjugacy invariants is also given. Krishnendu Gongopadhyay Copyright © 2012 Krishnendu Gongopadhyay. All rights reserved.