Ricci Solitons in α-Sasakian Manifolds. (8th August 2012)

• Record Type: Journal Article
• Authors: Ingalahalli, Gurupadavva; Bagewadi, C. S.
• Other Names: Schuller F. P. Academic Editor.; Strachan I. Academic Editor.
• Is Part Of: ISRN geometry. Volume 2012(2012)
• Publication Date: 2012-08-08
• Subjects: Geometry -- Periodicals; Topology -- Periodicals; Geometry; Topology; Periodicals; 516
• DOI: 10.5402/2012/421384
• Languages: English
• ISSNs: 2090-6307

Abstract

Abstract : 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 ℒ V g + 2 S 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.