- International Electronic Journal of Geometry
- Vol: 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 : 6 | Download : 5
Publication Date : 2021-04-15
Article Type : Research
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