A NOTE ON CONFORMAL VECTOR FIELDS ON A RIEMANNIAN MANIFOLD

被引：21

作者：

Deshmukh, Sharief ^{[1
]}

Al-Solamy, Falleh ^{[2
]}

机构：

[1] King Saud Univ, Coll Sci, Dept Math, Riyadh 11451, Saudi Arabia

[2] King Abdulaziz Univ, Fac Sci, Dept Math, Jeddah 21589, Saudi Arabia

来源：

COLLOQUIUM MATHEMATICUM | 2014年 / 136卷 / 01期

关键词：

conformal vector fields; Obata's theorem; phi-analytic conformal vector fields; DIFFERENTIAL-EQUATIONS;

D O I：

10.4064/cm136-1-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 phi-analytic conformal vector fields, study their properties, and obtain a characterization of n-spheres using these vector fields.

引用

页码：65 / 73

页数：9

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