Displaying similar documents to “Theorems concerning certain special tensor fields on Riemannian manifolds and their applications.”

Metrizability of connections on two-manifolds

Alena Vanžurová, Petra Žáčková (2009)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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We contribute to the reverse of the Fundamental Theorem of Riemannian geometry: if a symmetric linear connection on a manifold is given, find non-degenerate metrics compatible with the connection (locally or globally) if there are any. The problem is not easy in general. For nowhere flat 2 -manifolds, we formulate necessary and sufficient metrizability conditions. In the favourable case, we describe all compatible metrics in terms of the Ricci tensor. We propose an application in the...

On Riemann and Weyl Compatible Tensors

Ryszard Deszcz, Małgorzata Głogowska, Jan Jełowicki, Miroslava Petrović-Torgašev, Georges Zafindratafa (2013)

Publications de l'Institut Mathématique

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Killing tensors and warped product

Włodzimierz Jelonek (2000)

Annales Polonici Mathematici

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We present some examples of Killing tensors and give their geometric interpretation. We give new examples of non-compact complete and compact Riemannian manifolds whose Ricci tensor ϱ satisfies the condition X ϱ ( X , X ) = 2 / ( n + 2 ) X τ g ( X , X )