Generalized Ricci soliton and paracontact geometry

Title

Generalized Ricci soliton and paracontact geometry

Creator

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

Description

In the present paper, we study generalized Ricci soliton in the framework of paracontact metric manifolds. First, we prove that if the metric of a paracontact metric manifold M with Q?= ?Q is a generalized Ricci soliton (g,X) and if X? 0 is pointwise collinear to ?, then M is K-paracontact and ?-Einstein. Next, we consider closed generalized Ricci soliton on K-paracontact manifold and prove that it is Einstein provided ?(?+ 2 n?) ? 1. Next, we study K-paracontact metric as gradient generalized almost Ricci soliton and in this case we prove that (i) the scalar curvature r is constant and is equal to - 2 n(2 n+ 1) ; (ii) the squared norm of Ricci operator is constant and is equal to 4 n2(2 n+ 1) , provided ??? - 1. 2021, Instituto de Matemica e Estattica da Universidade de S Paulo.

Source

Sao Paulo Journal of Mathematical Sciences, Vol-15, No. 2, pp. 916-927.

Date

2021-01-01

Publisher

Springer Science and Business Media Deutschland GmbH

Subject

Generalized Ricci soliton; K-Paracontact manifold; Paracontact metric manifold; ParaSasakian manifold

Coverage

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

Rights

Restricted Access

Relation

ISSN: 19826907

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.1007/s40863-021-00260-1

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