1Department of Mathematics College of Science King Saud University P.O. Box 2455 Riyadh 11451, Saudi Arabia 2Department of Mathematics Faculty of Science King Abdulaziz University P.O. Box 80015 Jeddah 21589, Saudi Arabia
Colloquium Mathematicum, Tome 136 (2014) no. 1, pp. 65-73
We consider an $n$-dimensional compact Riemannian manifold $(M,g)$ and show that the presence of a non-Killing conformal vector field $\xi $ on $M$ that is also an eigenvector of the Laplacian operator acting on smooth vector fields with eigenvalue $\lambda >0 $, together with an upper bound on the energy of the vector field $\xi $, implies that $M$ is isometric to the $n$-sphere $S^{n}(\lambda )$. We also introduce the notion of $\varphi $-analytic conformal vector fields, study their properties, and obtain a characterization of $n$-spheres using these vector
fields.
Keywords:
consider n dimensional compact riemannian manifold presence non killing conformal vector field eigenvector laplacian operator acting smooth vector fields eigenvalue lambda together upper bound energy vector field implies isometric n sphere lambda introduce notion varphi analytic conformal vector fields study their properties obtain characterization n spheres using these vector fields
Affiliations des auteurs :
Sharief Deshmukh
1
;
Falleh Al-Solamy
2
1
Department of Mathematics College of Science King Saud University P.O. Box 2455 Riyadh 11451, Saudi Arabia
2
Department of Mathematics Faculty of Science King Abdulaziz University P.O. Box 80015 Jeddah 21589, Saudi Arabia
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Sharief Deshmukh; Falleh Al-Solamy. A note on conformal vector fields
on a Riemannian manifold. Colloquium Mathematicum, Tome 136 (2014) no. 1, pp. 65-73. doi: 10.4064/cm136-1-7
