Displaying similar documents to “On the concircular curvature tensor of a ( κ , μ ) -manifold.”

Extended Derdziński-Shen theorem for curvature tensors

Carlo Alberto Mantica, Luca Guido Molinari (2012)

Colloquium Mathematicae

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We extend a remarkable theorem of Derdziński and Shen, on the restrictions imposed on the Riemann tensor by the existence of a nontrivial Codazzi tensor. We show that the Codazzi equation can be replaced by a more general algebraic condition. The resulting extension applies both to the Riemann tensor and to generalized curvature tensors.

The conformal change of the metric of an almost Hermitian manifold applied to the antiholomorphic curvature tensor

Mileva Prvanović (2013)

Communications in Mathematics

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By using the technique of decomposition of a Hermitian vector space under the action of a unitary group, Ganchev [2] obtained a tensor which he named the Weyl component of the antiholomorphic curvature tensor. We show that the same tensor can be obtained by direct application of the conformal change of the metric to the antiholomorphic curvature tensor. Also, we find some other conformally curvature tensors and examine some relations between them.

Almost contact metric submersions and curvature tensors.

Tshikunguila Tshikuna-Matamba (2005)

Extracta Mathematicae

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It is known that L. Vanhecke, among other geometers, has studied curvature properties both on almost Hermitian and almost contact metric manifolds. The purpose of this paper is to interrelate these properties within the theory of almost contact metric submersions. So, we examine the following problem: Let f: M → B be an almost contact metric submersion. Suppose that the total space is a C(α)-manifold. What curvature properties do have the fibres or the base...