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São Paulo Journal of Mathematical Sciences
Article . 2021 . Peer-reviewed
License: Springer TDM
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image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
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Article . 2021
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Generalized Ricci soliton and paracontact geometry

Authors: Devaraja Mallesha Naik; V. Venkatesha; H. Aruna Kumara;

Generalized Ricci soliton and paracontact geometry

Abstract

In the present paper, the authors study generalized Ricci solitons in the framework of paracontact metric manifolds. It is interesting that the equation for a metric \(g\) to be a generalized Ricci soliton unifies various important equations such as: homothetic vector field, Killing vector field, Ricci soliton, metric projective structure equation in the projective class for which the Ricci tensor is skew-symmetric, the equation of vacuum near horizon geometry, the equation of Einstein-Weyl. In the first result of the paper, under assumptions, the authors obtain \(K\)-paracontact and \(\eta\)-Einstein manifolds, whenever they start with a paracontact metric manifold. In the second important result they assume conditions on the \(K\)-paracontact metric to obtain a Einstein metric. In the third main result of the work, the authors assume that the K-paracontact metric is a gradient generalized almost Ricci soliton and they obtain conditions on the scalar curvature and on the squared norm of the Ricci operator. Finally they compute some explicit examples.

Keywords

Special Riemannian manifolds (Einstein, Sasakian, etc.), paracontact metric manifold, General geometric structures on manifolds (almost complex, almost product structures, etc.), para-Sasakian manifold, \(K\)-paracontact manifold, Almost contact and almost symplectic manifolds, generalized Ricci soliton

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
Average
Average
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