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ISRN Geometry
Volume 2012 (2012), Article ID 421384, 13 pages
doi:10.5402/2012/421384
Ricci Solitons in -Sasakian Manifolds
Department of Mathematics, Kuvempu University, Shankaraghatta 577 451, India
Received 20 April 2012; Accepted 28 May 2012
Academic Editors: F. P. Schuller and I. Strachan
Copyright © 2012 Gurupadavva Ingalahalli and C. S. Bagewadi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We study Ricci solitons in -Sasakian manifolds. It is shown that a symmetric parallel second order-covariant tensor in a -Sasakian manifold is a constant multiple of the metric tensor. Using this, it is shown that if is parallel where is a given vector field, then is Ricci soliton. Further, by virtue of this result, Ricci solitons for -dimensional -Sasakian manifolds are obtained. Next, Ricci solitons for 3-dimensional -Sasakian manifolds are discussed with an example.