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Generalized Quasi-Einstein Metrics and Contact Geometry

Uday Chand De
경북대학교 자연과학대학 수학과|2022.09|Kyungpook Mathematical Journal|제62권 제3호|pp. 485-495|DOI https://doi.org/10.5666/KMJ.2022.62.3.485

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키워드

Sasakian manifoldsContact manifoldsGQE metricsAlmost contact manifoldsK-contact manifolds
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초록

The aim of this paper is to characterize K-contact and Sasakian manifolds whose metrics are generalized quasi-Einstein metric. It is proven that if the metric of a K-contact manifold is generalized quasi-Einstein metric, then the manifold is of constant scalar curvature and in the case of a Sasakian manifold the metric becomes Einstein under certain restriction on the potential function. Several corollaries have been provided. Finally, we consider Sasakian 3-manifold whose metric is generalized quasi-Einstein metric.

Abstract

The aim of this paper is to characterize K-contact and Sasakian manifolds whose metrics are generalized quasi-Einstein metric. It is proven that if the metric of a K-contact manifold is generalized quasi-Einstein metric, then the manifold is of constant scalar curvature and in the case of a Sasakian manifold the metric becomes Einstein under certain restriction on the potential function. Several corollaries have been provided. Finally, we consider Sasakian 3-manifold whose metric is generalized quasi-Einstein metric.

참고문헌 (28)

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