Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource Articles Article Faculty Publications -Articles Dublin Core The Dublin Core metadata element set is common to all Omeka records, including items, files, and collections. For more information see, http://dublincore.org/documents/dces/. Title A name given to the resource On an anti-torqued vector field on riemannian manifolds Subject The topic of the resource Concircular vector fields; Einstein manifolds; Fischermarsden equation; Scalar curvature; Torqued vector fields; Torse-forming vector fields Description An account of the resource 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. Creator An entity primarily responsible for making the resource Deshmukh S.; Al-Dayel I.; Naik D.M. Source A related resource from which the described resource is derived Mathematics, Vol-9, No. 18 Publisher An entity responsible for making the resource available MDPI Date A point or period of time associated with an event in the lifecycle of the resource 2021-01-01 Identifier An unambiguous reference to the resource within a given context <a href="https://doi.org/10.3390/math9182201" target="_blank" rel="noreferrer noopener">https://doi.org/10.3390/math9182201</a> <br /><br /><a href="https://www.scopus.com/inward/record.uri?eid=2-s2.0-85114743161&amp;doi=10.3390%2Fmath9182201&amp;partnerID=40&amp;md5=2d5b6f7e7ab4407b6c60eaa6d874a9bf" target="_blank" rel="noreferrer noopener">https://www.scopus.com/inward/record.uri?eid=2-s2.0-85114743161&amp;doi=10.3390%2fmath9182201&amp;partnerID=40&amp;md5=2d5b6f7e7ab4407b6c60eaa6d874a9bf</a> Rights Information about rights held in and over the resource All Open Access; Gold Open Access Relation A related resource ISSN: 22277390 Format The file format, physical medium, or dimensions of the resource Online Language A language of the resource English Type The nature or genre of the resource Article Coverage The spatial or temporal topic of the resource, the spatial applicability of the resource, or the jurisdiction under which the resource is relevant 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