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 Ricci solitons on Riemannian manifolds admitting certain vector field Subject The topic of the resource 53C21; 53C25; 53C44; Conformal vector field; Gradient Ricci almost soliton; Ricci almost soliton; Ricci soliton Description An account of the resource 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. Creator An entity primarily responsible for making the resource Naik D.M. Source A related resource from which the described resource is derived Ricerche di Matematica, Vol-73, No. 1, pp. 531-546. Publisher An entity responsible for making the resource available Springer-Verlag Italia s.r.l. Date A point or period of time associated with an event in the lifecycle of the resource 2024-01-01 Identifier An unambiguous reference to the resource within a given context <a href="https://doi.org/10.1007/s11587-021-00622-z" target="_blank" rel="noreferrer noopener">https://doi.org/10.1007/s11587-021-00622-z</a> <br /><br /><a href="https://www.scopus.com/inward/record.uri?eid=2-s2.0-85111133811&amp;doi=10.1007%2Fs11587-021-00622-z&amp;partnerID=40&amp;md5=ce065df5cc30619935f4dfed3ba4036a" target="_blank" rel="noreferrer noopener">https://www.scopus.com/inward/record.uri?eid=2-s2.0-85111133811&amp;doi=10.1007%2fs11587-021-00622-z&amp;partnerID=40&amp;md5=ce065df5cc30619935f4dfed3ba4036a</a> Rights Information about rights held in and over the resource Restricted Access Relation A related resource ISSN: 355038 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 Naik D.M., Department of Mathematics, CHRIST (Deemed to be University), Karnataka, Bengaluru, India