Topic
Ricci decomposition
About: Ricci decomposition is a research topic. Over the lifetime, 1972 publications have been published within this topic receiving 45295 citations.
Papers published on a yearly basis
Papers
More filters
13 Jun 2006
TL;DR: In this paper, the Ricci curvature of a compact Riemannian manifold was shown to be greater than the Lie derivative of the metric with respect to some fixed smooth vector field.
Abstract: Let the Ricci curvature of a compact Riemannian manifold be greater, at every point, than the Lie derivative of the metric with respect to some fixed smooth vector field. It is shown that the fundamental group then has only finitely many conjugacy classes. This applies, in particular, to all compact shrinking Ricci solitons.
40 citations
TL;DR: In this paper, it was shown that the wave front set of the solenoidal part of a field f can be recovered from the ray transform If, and an explicit procedure for recovering the wavefront set was given.
Abstract: We study on a compact Riemannian manifold with boundary the ray transform I which integrates symmetric tensor fields over geodesics. A tensor field is said to be a nontrivial ghost if it is in the kernel of I and is L2-orthogonal to all potential fields. We prove that a nontrivial ghost is smooth in the case of a simple metric. This implies that the wave front set of the solenoidal part of a field f can be recovered from the ray transform If. We give an explicit procedure for recovering the wave front set.
40 citations
40 citations
39 citations