We derive matter collineations for some static spherically symmetric spacetimes and compare the results with Killing, Ricci and Curvature symmetries. We conclude that matter and Ricci collineations are not, in general, the same.

Abstract We introduce the notion of rigidity for harmonic-Ricci solitons and provide some characterizations rigidity, generalizing known results Ricci solitons. In complete case we restrict to steady shrinking gradient solitons, while in compact treat general without further assumptions. show that can be traced back vanishing certain modified curvature tensors take into account geometry a Riema...

We give an elementary construction of symplectic connections through reduction. This provides an elegant description of a class of symmetric spaces and gives examples of symplectic connections with Ricci type curvature, which are not locally symmetric; the existence of such symplectic connections was unknown. Key-words: Marsden-Weinstein reduction, symplectic connections, symmetric spaces MSC 2...

In [H4], Hamilton determined a sharp tensor Harnack inequality for complete solutions of the Ricci flow with non-negative curvature operator. This Harnack inequality is of critical importance to the understanding of singularities of the Ricci flow, as is evident from its numerous applications in [H3], [H5], [H6], and [H7]. Moreover, according to Hamilton, the discovery of a Harnack inequality i...

We consider Bel–Robinson-like higher derivative conserved two-index tensors H µν in simple matter models, following a recently suggested Maxwell field version. In flat space, we show that they are essentially equivalent to the true stress-tensors. In curved Ricci-flat backgrounds it is possible to redefine H µν so as to overcome non-commutativity of covariant derivatives, and maintain conservat...

Walker manifolds of signature (2, 2) have been used by many authors to provide examples of Osserman and of conformal Osserman manifolds of signature (2, 2). We study questions of geodesic completeness and Ricci blowup in this context.

We establish codimension 4 regularity of noncollapsed sequences metrics with bounds on natural generalizations the Ricci tensor. obtain a priori $$L^2$$ curvature estimates such spaces, diffeomorphism finiteness results and rigidity theorems as corollaries.