Remarks on Scalar Curvature and Concircular Field Equation

Year 2021, Volume: 14 Issue: 1, 121 - 124, 15.04.2021

Ramesh Sharma Sharief Deshmukh

https://doi.org/10.36890/iejg.906792

Abstract

We show that the scalar curvature of a Riemannian manifold $M$ is constant if it satisfies (i) the concircular field equation and $M$ is compact, (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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