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Dergiler / International Electronic Journal of Geometry / 2021 / Cilt: 14 - Sayı: 1

Remarks on Scalar Curvature and Concircular Field Equation

Ramesh SHARMA
Sharief DESHMUKH
Sayfa
121–124
Yayın Tarihi
2022-10-18
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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.

📌 3 Maddede Bu Makale

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Amaç & Hipotez: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.
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Temel Bulgular & Veri: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.
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Sonuç & Katkı: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.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Scalar curvature · concircular vector field · concircular scalar equation

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.

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Bu Makaleye Atıf Yap

SHARMA, R., DESHMUKH, S. (2022). Remarks on Scalar Curvature and Concircular Field Equation. International Electronic Journal of Geometry, Cilt: 14 - Sayı: 1, 121–124. https://ajindex.com/articles/539566

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Kaynakça (10)

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