Certain property of the Ricci tensor on Sasakian manifolds

Alignment classification of tensors on Lorentzian manifolds of arbitrary dimension is summarized. This classification scheme is then applied to the case of the Weyl tensor and it is shown that in four dimensions it is equivalent to the well known Petrov classification. The approaches using Bel-Debever criteria and principal null directions of the superenergy tensor are also discussed.

From the Eisenhart problem to Ricci solitons in $f$ -Kenmotsu manifolds.

Călin, Constantin, Crasmareanu, Mircea (2010)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

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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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On some generalisation of recurrent manifolds.

Ewert-Krzemieniewski, Stanisław (1993)

Mathematica Pannonica

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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 $\nabla_{X} ϱ (X, X) = 2 / (n + 2) X τ g (X, X)$

On Riemannian manifolds satisfying a certain curvature condition imposed on the Weyl curvature tensor

Filip Defever, Ryszard Deszcz (1993)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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