Remarks on Scalar Curvature and Concircular Field Equation

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International Electronic Journal of Geometry
Volume:14 Issue:1
Remarks on Scalar Curvature and Concircular Field Equation

Remarks on Scalar Curvature and Concircular Field Equation

Authors : Ramesh SHARMA, Sharief DESHMUKH

Pages : 121-124

Doi:10.36890/iejg.906792

View : 46 | Download : 11

Publication Date : 2021-04-15

Article Type : Research Paper

Abstract :We show that the scalar curvature of a Riemannian manifold $M$ is constant if it satisfies insert ignore into journalissuearticles values(i); the concircular field equation and $M$ is compact, insert ignore into journalissuearticles values(ii); the special concircular field equation. Finally, we show that, if a complete connected Riemannian manifold admits a concircular non-isometric vector field leaving the scalar curvature invariant, and the conformal function is special concircular, then the scalar curvature is a constant.
Keywords : Scalar curvature, concircular vector field, concircular scalar equation, gradient Yamabe soliton

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