Certain types of metrics on almost coKler manifolds

Title

Certain types of metrics on almost coKler manifolds

Creator

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

Description

In this paper, we study an almost coKler manifold admitting certain metrics such as ? -Ricci solitons, satisfying the critical point equation (CPE) or Bach flat. First, we consider a coKler 3-manifold (M,g) admitting a ? -Ricci soliton (g,X) and we show in this case that either M is locally flat or X is an infinitesimal contact transformation. Next, we study non-coKler (?, ?) -almost coKler metrics as CPE metrics and prove that such a g cannot be a solution of CPE with non-trivial function f. Finally, we prove that a (?, ?) -almost coKler manifold (M,g) is coKler if either M admits a divergence free Cotton tensor or the metric g is Bach flat. In contrast to this, we show by a suitable example that there are Bach flat almost coKler manifolds which are non-coKler. 2021, Fondation Carl-Herz and Springer Nature Switzerland AG.

Source

Annales Mathematiques du Quebec, Vol-47, No. 2, pp. 331-347.

Date

2023-01-01

Publisher

Springer Science and Business Media Deutschland GmbH

Subject

Almost coKler manifold; Bach tensor; Cotton tensor; Critical point equation; ? -Ricci soliton

Coverage

Naik D.M., Department of Mathematics, Kuvempu University, Karnataka, Shivamogga, India, Department of Mathematics, CHRIST (Deemed to be University), Karnataka, Bangalore, India; Venkatesha V., Department of Mathematics, Kuvempu University, Karnataka, Shivamogga, India; Kumara H.A., Department of Mathematics, Kuvempu University, Karnataka, Shivamogga, India

Rights

Restricted Access

Relation

ISSN: 21954755

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.1007/s40316-021-00162-w

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