Conformal gradient vector fields on a compact Riemannian manifold

• Autorzy: Sharief Deshmukh , Falleh Al-Solamy
• Języki publikacji: EN

Abstrakty

EN

It is proved that if an n-dimensional compact connected Riemannian manifold (M,g) with Ricci curvature Ric satisfying
0 < Ric ≤ (n-1)(2-nc/λ₁)c
for a constant c admits a nonzero conformal gradient vector field, then it is isometric to Sⁿ(c), where λ₁ is the first nonzero eigenvalue of the Laplacian operator on M. Also, it is observed that existence of a nonzero conformal gradient vector field on an n-dimensional compact connected Einstein manifold forces it to have positive scalar curvature and ultimately to be isometric to Sⁿ(c), where n(n-1)c is the scalar curvature of the manifold.

Kategorie tematyczne

• 53C20: Global Riemannian geometry, including pinching

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2008
• Tom: 112
• Numer: 1
• Strony: 157-161

Daty

wydano

2008

Twórcy

autor

Sharief Deshmukh

• Department of Mathematics, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

autor

Falleh Al-Solamy

• Department of Mathematics, King Abdul Aziz University, P.O. Box 80015, Jeddah 21589, Saudi Arabia

Identyfikatory

DOI

10.4064/cm112-1-8