Displaying similar documents to “The Evolution of the Weyl Tensor under the Ricci Flow”

The Cotton Tensor and the Ricci Flow

Carlo Mantegazza, Samuele Mongodi, Michele Rimoldi (2017)

Geometric Flows

Similarity:

We compute the evolution equation of the Cotton and the Bach tensor under the Ricci flow of a Riemannian manifold, with particular attention to the three dimensional case, and we discuss some applications.

On a generalized class of recurrent manifolds

Absos Ali Shaikh, Ananta Patra (2010)

Archivum Mathematicum

Similarity:

The object of the present paper is to introduce a non-flat Riemannian manifold called hyper-generalized recurrent manifolds and study its various geometric properties along with the existence of a proper example.

On generalized M-projectively recurrent manifolds

Uday Chand De, Prajjwal Pal (2014)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

Similarity:

The purpose of the present paper is to study generalized M-projectively recurrent manifolds. Some geometric properties of generalized M projectively recurrent manifolds have been studied under certain curvature conditions. An application of such a manifold in the theory of relativity has also been shown. Finally, we give an example of a generalized M-projectively recurrent manifold.

Almost-Einstein manifolds with nonnegative isotropic curvature

Harish Seshadri (2010)

Annales de l’institut Fourier

Similarity:

Let ( M , g ) , n ≥ 4 , be a compact simply-connected Riemannian n -manifold with nonnegative isotropic curvature. Given 0 < l ≤ L , we prove that there exists ε = ε ( l , L , n ) satisfying the following: If the scalar curvature s of g satisfies l ≤ s ≤ L and the Einstein tensor satisfies Ric - s n g ≤ ε then M is diffeomorphic to a symmetric space of compact type. This is related to the result of S. Brendle on the metric rigidity of Einstein manifolds with nonnegative isotropic curvature. ...