Generalized quasi-Einstein manifolds with harmonic Weyl tensor

2010/12/31 by Giovanni Catino · 6 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.1007/s00209-011-0888-5

published as Math. Z., 271 (2012), no. 3-4, 751-756

arxiv created 2011/03/13 · arxiv updated 2014/10/10

Abstract

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.

Cited by

• On critical point equation of compact manifolds with zero radial Weyl curvature
• Quasi-Einstein manifolds with Harmonic Weyl curvature
• Characterization of generalized quasi-Einstein manifolds and modified gravity
• Local Structure of Gradient Almost Ricci Solitons with Harmonic Weyl Tensor
• Rigidity of complete non-compact generalized m-quasi-Einstein manifolds
• Half conformally flat gradient Ricci almost solitons. [europepmc]