Generalized Quasi-Einstein Metrics and Contact Geometry

Biswas G. G., De U. C., YILDIZ A.

KYUNGPOOK MATHEMATICAL JOURNAL, vol.62, no.3, pp.485-495, 2022 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 62 Issue: 3
  • Publication Date: 2022
  • Doi Number: 10.5666/kmj.2022.62.3.485
  • Journal Name: KYUNGPOOK MATHEMATICAL JOURNAL
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.485-495
  • Keywords: GQE metrics, Almost contact manifolds, Contact manifolds, K-contact manifolds, Sasakian manifolds, K-CONTACT, GRADIENT, MANIFOLDS, (K
  • Inonu University Affiliated: No

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.