Remarks on Scalar Curvature and Concircular Field Equation

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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International Electronic Journal of Geometry-Cover

Yayın Aralığı: Yılda 2 Sayı
Başlangıç: 2008
Yayıncı: Prof.Dr. H.Hilmi Hacısalioğlu

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