Generalized Ricci solitons on Riemannian manifolds admitting concurrent-recurrent vector field

Title

Generalized Ricci solitons on Riemannian manifolds admitting concurrent-recurrent vector field

Creator

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

Description

Let (M,g) be a Riemannian manifold admitting a concurrent-recurrent vector field ?. We prove that if the metric g is a generalized Ricci soliton such that the potential field V is a conformal vector field, then M is Einstein. Next we show that if the metric of M is a gradient generalized Ricci soliton, then either of these three occurs: (i) ?? is invariant along gradient of potential function; (ii) M is Einstein; (iii) the potential vector field is pointwise collinear to concurrent-recurrent vector field ?. Finally, we investigate gradient generalized Ricci soliton on a Riemannian manifold (M,g) admitting a unit parallel vector field, and in this case we show that if g is a non-steady gradient generalized Ricci soliton, then the Ricci tensor satisfies Ric=-??{g-?????}, where ?? is the canonical 1-form associated to ?. 2022, The Author(s), under exclusive licence to The Forum DAnalystes.

Source

Journal of Analysis, Vol-30, No. 3, pp. 1023-1031.

Date

2022-01-01

Publisher

Springer Science and Business Media B.V.

Subject

Conformal vector field; Generalized Ricci soliton; Gradient generalized Ricci soliton

Coverage

Naik D.M., Department of Mathematics, Centre for Mathematical Needs, CHRIST (Deemed to be University), Karnataka, Bengaluru, 560029, India; Kumara H.A., Department of Mathematics, Kuvempu University, Karnataka, Shivamogga, 577451, India; Venkatesha V., Department of Mathematics, Kuvempu University, Karnataka, Shivamogga, 577451, India

Rights

Restricted Access

Relation

ISSN: 9713611

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.1007/s41478-022-00387-0

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