http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2013 , Hindawi Publishing Corporation . All rights reserved. Thu, 16 May 2013 14:30:00 +0000 http://www.hindawi.com/journals/geometry/2013/549198/ We construct a 4-parametric family of combinatorial closed 3-manifolds, obtained by glueing together in pairs the boundary faces of polyhedral 3-balls. Then, we obtain geometric presentations of the fundamental groups of these manifolds and determine the corresponding split extension groups. Finally, we prove that the considered manifolds are cyclic coverings of the 3-sphere branched over well-specified -knots, including torus knots and Montesinos knots. Agnese Ilaria Telloni Copyright © 2013 Agnese Ilaria Telloni. All rights reserved. Tue, 30 Apr 2013 08:13:05 +0000 http://www.hindawi.com/journals/geometry/2013/654780/ We study sectional curvature, Ricci tensor, and scalar curvature of submanifolds of generalized -space forms. Then we give an upper bound for foliate -horizontal (and vertical) CR-submanifold of a generalized -space form and an upper bound for minimal -horizontal (and vertical) CR-submanifold of a generalized -space form. Finally, we give the same results for special cases of generalized -space forms such as -space forms, generalized Sasakian space forms, Sasakian space forms, Kenmotsu space forms, cosymplectic space forms, and almost -manifolds. Mahmood Jaafari Matehkolaee Copyright © 2013 Mahmood Jaafari Matehkolaee. All rights reserved. Sun, 14 Apr 2013 09:20:34 +0000 http://www.hindawi.com/journals/geometry/2013/364301/ A canonical vector field on the tangent bundle is a vector field defined by an invariant coordinate construction. In this paper, a complete classification of canonical vector fields on tangent bundles, depending on vector fields defined on their bases, is obtained. It is shown that every canonical vector field is a linear combination with constant coefficients of three vector fields: the variational vector field (canonical lift), the Liouville vector field, and the vertical lift of a vector field on the base of the tangent bundle. Tongzhu Li and Demeter Krupka Copyright © 2013 Tongzhu Li and Demeter Krupka. All rights reserved. Sun, 07 Apr 2013 16:24:39 +0000 http://www.hindawi.com/journals/geometry/2013/902092/ The notion of a generalized harmonic inverse mean curvature surface in the Euclidean four-space is introduced. A backward Bäcklund transform of a generalized harmonic inverse mean curvature surface is defined. A Darboux transform of a generalized harmonic inverse mean curvature surface is constructed by a backward Bäcklund transform. For a given isothermic harmonic inverse mean curvature surface, its classical Darboux transform is a harmonic inverse mean curvature surface. Then a transform of a solution to the Painlevé III equation in trigonometric form is defined by a classical Darboux transform of a harmonic inverse mean curvature surface of revolution. Katsuhiro Moriya Copyright © 2013 Katsuhiro Moriya. All rights reserved. Thu, 14 Mar 2013 19:15:39 +0000 http://www.hindawi.com/journals/geometry/2013/715907/ Fix integers and . Let be a degree homogeneous polynomial in variables. Here, we prove that is the sum of at most -powers of linear forms (of course, this inequality is nontrivial only if .) E. Ballico Copyright © 2013 E. Ballico. All rights reserved. Wed, 06 Feb 2013 15:40:44 +0000 http://www.hindawi.com/journals/geometry/2013/649168/ We consider an n-dimensional Finsler space with the metric , where is an th-root metric and is a Riemannian metric. We call such space as an R-Randers th-root space. We obtain the expressions for the fundamental metric tensor, Cartan tensor, geodesic spray coefficients, and the coefficients of nonlinear connection in an R-Randers th-root space. Some other properties of such space have also been discussed. P. N. Pandey and Shivalika Saxena Copyright © 2013 P. N. Pandey and Shivalika Saxena. All rights reserved. Mon, 04 Feb 2013 09:27:29 +0000 http://www.hindawi.com/journals/geometry/2013/292691/ We study generalized projectively symmetric spaces. We first study some geometric properties of projectively symmetric spaces and prove that any such space is projectively homogeneous and under certain conditions the projective curvature tensor vanishes. Then we prove that given any regular projective s-space (, ), there exists a projectively related connection , such that (, ) is an affine s-manifold. Dariush Latifi and Asadollah Razavi Copyright © 2013 Dariush Latifi and Asadollah Razavi. All rights reserved. Wed, 30 Jan 2013 12:08:36 +0000 http://www.hindawi.com/journals/geometry/2013/369420/ We study the Galois group defined by a point projection for plane curve. First, we present a sufficient condition that the group is primitive and then determine the structure at each point for some self-dual curves. Hiroyuki Hayashi and Hisao Yoshihara Copyright © 2013 Hiroyuki Hayashi and Hisao Yoshihara. All rights reserved. Wed, 30 Jan 2013 11:39:07 +0000 http://www.hindawi.com/journals/geometry/2013/106393/ We study Lagrange spaces with -metric, where is a cubic metric and is a 1-form. We obtain fundamental metric tensor, its inverse, Euler-Lagrange equations, semispray coefficients, and canonical nonlinear connection for a Lagrange space endowed with a -metric. Several other properties of such space are also discussed. Suresh K. Shukla and P. N. Pandey Copyright © 2013 Suresh K. Shukla and P. N. Pandey. All rights reserved. Sun, 13 Jan 2013 09:52:20 +0000 http://www.hindawi.com/journals/geometry/2013/373701/ This paper is devoted to obtain the one-dimensional group invariant solutions of the two-dimensional Ricci flow ((2D) Rf) equation. By classifying the orbits of the adjoint representation of the symmetry group on its Lie algebra, the optimal system of one-dimensional subalgebras of the ((2D) Rf) equation is obtained. For each class, we will find the reduced equation by the method of similarity reduction. By solving these reduced equations, we will obtain new sets of group invariant solutions for the ((2D) Rf) equation. Mehdi Nadjafikhah and Mehdi Jafari Copyright © 2013 Mehdi Nadjafikhah and Mehdi Jafari. All rights reserved. Sun, 13 Jan 2013 09:50:41 +0000 http://www.hindawi.com/journals/geometry/2013/497191/ Making use of the linear operator defined by (Frasin 2012), we introduce the class of meromorphically -valent functions in the punctured unit disk . Furthermore, we obtain some sufficient conditions for starlikeness and close-to-convexity for functions belonging to this class. Several corollaries and consequences of the main results are also considered. B. A. Frasin, Tariq Al-Hawary, and M. Darus Copyright © 2013 B. A. Frasin et al. All rights reserved. Thu, 10 Jan 2013 14:44:33 +0000 http://www.hindawi.com/journals/geometry/2013/897320/ In 2005, David Cox and Jerry Shurman proved that the curves they call -clovers can be subdivided into equal lengths (for certain values of ) by origami, in the cases where , 2, 3, and 4. In this paper, we expand their work to include the 6-clover. Joel C. Langer and David A. Singer Copyright © 2013 Joel C. Langer and David A. Singer. All rights reserved.