ItemArticle

On an anti-torqued vector field on riemannian manifolds

Title
On an anti-torqued vector field on riemannian manifolds
Creator
Deshmukh S.; Al-Dayel I.; Naik D.M.
Description
A torqued vector field ? is a torse-forming vector field on a Riemannian manifold that is orthogonal to the dual vector field of the 1-form in the definition of torse-forming vector field. In this paper, we introduce an anti-torqued vector field which is opposite to torqued vector field in the sense it is parallel to the dual vector field to the 1-form in the definition of torse-forming vector fields. It is interesting to note that anti-torqued vector fields do not reduce to concircular vector fields nor to Killing vector fields and thus, give a unique class among the classes of special vector fields on Riemannian manifolds. These vector fields do not exist on compact and simply connected Riemannian manifolds. We use anti-torqued vector fields to find two characterizations of Euclidean spaces. Furthermore, a characterization of an Einstein manifold is obtained using the combination of a torqued vector field and FischerMarsden equation. We also find a condition under which the scalar curvature of a compact Riemannian manifold admitting an anti-torqued vector field is strictly negative. 2021 by the authors. Licensee MDPI, Basel, Switzerland.
Source
Mathematics, Vol-9, No. 18
Date
2021-01-01
Publisher
MDPI
Subject
Concircular vector fields; Einstein manifolds; Fischermarsden equation; Scalar curvature; Torqued vector fields; Torse-forming vector fields
Coverage
Deshmukh S., Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia; Al-Dayel I., Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University, P.O. Box 65892, Riyadh, 11566, Saudi Arabia; Naik D.M., Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, 560029, India
Rights
All Open Access; Gold Open Access
Relation
ISSN: 22277390
Format
Online
Language
English
Type
Article

Collection

Articles

Citation

Deshmukh S.; Al-Dayel I.; Naik D.M., “On an anti-torqued vector field on riemannian manifolds,” CHRIST (Deemed To Be University) Institutional Repository, accessed February 27, 2025, https://archives.christuniversity.in/items/show/15685.

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