Topic
Ricci decomposition
About: Ricci decomposition is a research topic. Over the lifetime, 1972 publications have been published within this topic receiving 45295 citations.
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TL;DR: In this article, the Yano-type Finsler connection was used to derive an intrinsic expression of Douglas' famous projective curvature tensor and also represented it in terms of the Berwald connection.
Abstract: After a careful study of the mixed curvatures of the Berwald-type (in particular, Berwald) connections, we present an axiomatic description of the so-called Yano-type Finsler connections. Using the Yano connection, we derive an intrinsic expression of Douglas' famous projective curvature tensor and we also represent it in terms of the Berwald connection. Utilizing a clever observation of Z. Shen, we show in a coordinate-free manner that a “spray manifold” is projectively equivalent to an affinely connected manifold iff its Douglas tensor vanishes. From this result we infer immediately that the vanishing of the Douglas tensor implies that the projective Weyl tensor of the Berwald connection “depends only on the position”
9 citations
TL;DR: In this article, the existence of LP-Sasakian manifold with Ricci tensor tensors is studied with several non-trivial examples, including generalized Ricci recurrent LP-sakian manifolds with various examples.
Abstract: The object of the present paper is to provide the existence of LP-Sasakian manifolds with ·-recurrent, ·-parallel, `-recurrent, `- parallel Ricci tensor with several non-trivial examples Also generalized Ricci recurrent LP-Sasakian manifolds are studied with the existence of various examples
9 citations
TL;DR: In this article, the authors derived a bound on the coupling constant between the sigma-field and the metric tensor using the theory of harmonic maps, and constructed new explicit solutions of the model.
Abstract: We discuss the four-dimensional nonlinear sigma-model with an internalO(n) invariance coupled to the metric tensor field satisfying Einstein equations. We derive a bound on the coupling constant between the sigma-field and the metric tensor using the theory of harmonic maps. A special attention is paid to Einstein spaces and some new explicit solutions of the model are constructed.
9 citations
01 Jan 2011
TL;DR: In this paper, it was proved that a compact φ-conharmonically flat K-contact manifold with regular contact vector field is a principal S1-bundle over an almost Kaehler space of constant holomorphic sectional curvature.
Abstract: Some necessary and/or sufficient condition(s) for K-contact and/or Sasakian manifolds to be quasi conharmonically flat, ξ-conharmonically flat and φ-conharmonically flat are obtained. In last, it is proved that a compact φ-conharmonically flat K-contact manifold with regular contact vector field is a principal S1-bundle over an almost Kaehler space of constant holomorphic sectional curvature ( 3− 2 2n−1 ) . 2010 Mathematics Subject Classification: 53C25, 53D10, 53D15
9 citations
01 Feb 1978
TL;DR: In this article, it was shown that the decomposition of tensor products Vx ® Vr for all dominant integral weights t may be derived from those for a finite set of such r.
Abstract: Let Vx be a finite dimensional irreducible module for a complex semisimple Lie algebra. It is shown that the decomposition of tensor products Vx ® Vr for all dominant integral weights t may be derived from those for a finite set of such r. An explicit choice of such a finite set (depending on X) is given.
9 citations