Ricci solitons on Riemannian manifolds admitting certain vector field

Title

Ricci solitons on Riemannian manifolds admitting certain vector field

Creator

Naik D.M.

Description

In this paper, we initiate the study of impact of the existence of a unit vector ?, called a concurrent-recurrent vector field, on the geometry of a Riemannian manifold. Some examples of these vector fields are provided on Riemannian manifolds, and basic geometric properties of these vector fields are derived. Next, we characterize Ricci solitons on 3-dimensional Riemannian manifolds and gradient Ricci almost solitons on a Riemannian manifold (of dimension n) admitting a concurrent-recurrent vector field. In particular, it is proved that the Riemannian 3-manifold equipped with a concurrent-recurrent vector field is of constant negative curvature -?2 when its metric is a Ricci soliton. Further, it has been shown that a Riemannian manifold admitting a concurrent-recurrent vector field, whose metric is a gradient Ricci almost soliton, is Einstein. Universitdegli Studi di Napoli "Federico II" 2021.

Source

Ricerche di Matematica, Vol-73, No. 1, pp. 531-546.

Date

2024-01-01

Publisher

Springer-Verlag Italia s.r.l.

Subject

53C21; 53C25; 53C44; Conformal vector field; Gradient Ricci almost soliton; Ricci almost soliton; Ricci soliton

Coverage

Naik D.M., Department of Mathematics, CHRIST (Deemed to be University), Karnataka, Bengaluru, India

Rights

Restricted Access

Relation

ISSN: 355038

Format

Online

Language

English

Type

Article

Identifier

https://doi.org/10.1007/s11587-021-00622-z

https://www.scopus.com/inward/record.uri?eid=2-s2.0-85111133811&doi=10.1007%2fs11587-021-00622-z&partnerID=40&md5=ce065df5cc30619935f4dfed3ba4036a