The geometry of closed conformal vector fields on Riemannian spaces |
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Authors: | A Caminha |
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Institution: | 1.Departamento de Matemática,Universidade Federal do Ceará,Fortaleza, Ceará,Brazil |
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Abstract: | In this paper we examine different aspects of the geometry of closed conformal vector fields on Riemannian manifolds. We begin
by getting obstructions to the existence of closed conformal and nonparallel vector fields on complete manifolds with nonpositive
Ricci curvature, thus generalizing a theorem of T.K. Pan. Then we explain why it is so difficult to find examples, other than
trivial ones, of spaces having at least two closed, conformal and homothetic vector fields. We then focus on isometric immersions,
firstly generalizing a theorem of J. Simons on cones with parallel mean curvature to spaces furnished with a closed, Ricci
null conformal vector field; then we prove general Bernstein-type theorems for certain complete, not necessarily cmc, hypersurfaces
of Riemannian manifolds furnished with closed conformal vector fields. In particular, we obtain a generalization of theorems
J. Jellett and A. Barros and P. Sousa for complete cmc radial graphs over finitely punctured geodesic spheres of Riemannian
space forms. |
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Keywords: | |
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