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.
Scalar curvature concircular vector field concircular scalar equation gradient Yamabe soliton
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Araştırma Makalesi |
Yazarlar | |
Yayımlanma Tarihi | 15 Nisan 2021 |
Kabul Tarihi | 26 Aralık 2020 |
Yayımlandığı Sayı | Yıl 2021 Cilt: 14 Sayı: 1 |