A note on conformal vector fields on a Riemannian manifold

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

Abstrakty

EN

We consider an n-dimensional compact Riemannian manifold (M,g) and show that the presence of a non-Killing conformal vector field ξ on M that is also an eigenvector of the Laplacian operator acting on smooth vector fields with eigenvalue λ > 0, together with an upper bound on the energy of the vector field ξ, implies that M is isometric to the n-sphere Sⁿ(λ). We also introduce the notion of φ-analytic conformal vector fields, study their properties, and obtain a characterization of n-spheres using these vector fields.

Kategorie tematyczne

• 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions
• 53C24: Rigidity results
• 53A30: Conformal differential geometry

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2014
• Tom: 136
• Numer: 1
• Strony: 65-73

Daty

wydano

2014

Twórcy

autor

Sharief Deshmukh

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

autor

Falleh Al-Solamy

• Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80015, Jeddah 21589, Saudi Arabia

Identyfikatory

DOI

10.4064/cm136-1-7