ON SOME INFINITESIMAL AUTOMORPHISMS OF RIEMANNIAN FOLIATION
In Riemannian foliation, a transverse affine vector field preserves the curvature and its covariant derivatives. In this paper we solve the converse problem. Actually, we show that an infinitesimal automorphism of a Riemannian foliation which preserves the curvature and its covariant derivatives induces a transverse almost homothetic vector field. If in addition the manifold is closed and the foliation is irreducible harmonic , then a such infinitesimal automorphism induces a transverse killing vector field.
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| Main Authors: | , |
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| Format: | Digital revista |
| Language: | English |
| Published: |
Universidad Católica del Norte, Departamento de Matemáticas
2007
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| Online Access: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172007000100001 |
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| Summary: | In Riemannian foliation, a transverse affine vector field preserves the curvature and its covariant derivatives. In this paper we solve the converse problem. Actually, we show that an infinitesimal automorphism of a Riemannian foliation which preserves the curvature and its covariant derivatives induces a transverse almost homothetic vector field. If in addition the manifold is closed and the foliation is irreducible harmonic , then a such infinitesimal automorphism induces a transverse killing vector field. |
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