Generalized quasi-Einstein manifolds with harmonic Weyl tensor

Details Generalized quasi-Einstein manifolds with harmonic Weyl tensor Generalized quasi-Einstein manifolds with harmonic Weyl tensor

2010-12-24

arxiv.org/abs/1012.5405v3

Mathematics

Differential Geometry

Scientific paper

In this paper we introduce the notion of generalized quasi--Einstein manifold, that generalizes the concepts of Ricci soliton, Ricci almost soliton and quasi--Einstein manifolds. We prove that a complete generalized quasi--Einstein manifold with harmonic Weyl tensor and with zero radial Weyl curvature, is locally a warped product with $(n-1)$--dimensional Einstein fibers. In particular, this implies a local characterization for locally conformally flat gradient Ricci almost solitons, similar to that proved for gradient Ricci solitons.

Affiliated with

Also associated with

No associations

Rating

Generalized quasi-Einstein manifolds with harmonic Weyl tensor does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Generalized quasi-Einstein manifolds with harmonic Weyl tensor, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Generalized quasi-Einstein manifolds with harmonic Weyl tensor will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-643411