Ricci solitons and certain related metrics on almost co-kaehler manifolds

Title

Ricci solitons and certain related metrics on almost co-kaehler manifolds

Creator

Naik D.M.; Venkatesha V.; Aruna Kumara H.

Description

In the paper, we study a Ricci soliton and a generalized m-quasi-Einstein metric on almost co-Kaehler manifold M satisfying a nullity condition. First, we consider a non-co-Kaehler (?, )-almost co-Kaehler metric as a Ricci soliton and prove that the soliton is expanding with ? = ?2n? and the soliton vector field X leaves the structure tensors ?, ? and ? invariant. This result extends Theorem 5.1 of [32]. We construct an example to show the existence of a Ricci soliton on M. Finally, we prove that if M is a generalized (?, )-almost co-Kaehler manifold of dimension higher than 3 such that h ? 0, then the metric of M can not be a generalized m-quasi-Einstein metric, and this recovers the recent result of Wang [37, Theorem 4.1] as a special case. Devaraja Mallesha Naik, V. Venkatesha, and H. Aruna Kumara, 2020.

Source

Journal of Mathematical Physics, Analysis, Geometry, Vol-16, No. 4, pp. 402-417.

Date

2020-01-01

Publisher

B.Verkin Institute for Low Temperature Physics and Engineering of the NAS of Ukraine

Subject

(?,)-nullity distribution; Almost co-Kaehler manifold; Generalized m-quasi-Einstein metric; Ricci soliton

Coverage

Naik D.M., Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, Karnataka, 560029, India; Venkatesha V., Department of Mathematics, Kuvempu University, Shankaraghatta, Karnataka, 577 451, India; Aruna Kumara H., Department of Mathematics, Kuvempu University, Shankaraghatta, Karnataka, 577 451, India

Rights

All Open Access; Bronze Open Access

Relation

ISSN: 18129471

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.15407/MAG16.04.402

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