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 ind...

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Autores principales:	CHAOUCH,MOHAMET AlÍ, TORKI - HAMZA,NABILA
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2007
Materias:	Riemannian foliation Harmonic foliation Irreducible foliation Transverse vector field
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172007000100001
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spelling	oai:scielo:S0716-091720070001000012018-10-30ON SOME INFINITESIMAL AUTOMORPHISMS OF RIEMANNIAN FOLIATIONCHAOUCH,MOHAMET AlÍTORKI - HAMZA,NABILA Riemannian foliation Harmonic foliation Irreducible foliation Transverse vector field 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.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.26 n.1 20072007-05-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172007000100001en10.4067/S0716-09172007000100001
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Riemannian foliation Harmonic foliation Irreducible foliation Transverse vector field
spellingShingle	Riemannian foliation Harmonic foliation Irreducible foliation Transverse vector field CHAOUCH,MOHAMET AlÍ TORKI - HAMZA,NABILA ON SOME INFINITESIMAL AUTOMORPHISMS OF RIEMANNIAN FOLIATION
description	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.
author	CHAOUCH,MOHAMET AlÍ TORKI - HAMZA,NABILA
author_facet	CHAOUCH,MOHAMET AlÍ TORKI - HAMZA,NABILA
author_sort	CHAOUCH,MOHAMET AlÍ
title	ON SOME INFINITESIMAL AUTOMORPHISMS OF RIEMANNIAN FOLIATION
title_short	ON SOME INFINITESIMAL AUTOMORPHISMS OF RIEMANNIAN FOLIATION
title_full	ON SOME INFINITESIMAL AUTOMORPHISMS OF RIEMANNIAN FOLIATION
title_fullStr	ON SOME INFINITESIMAL AUTOMORPHISMS OF RIEMANNIAN FOLIATION
title_full_unstemmed	ON SOME INFINITESIMAL AUTOMORPHISMS OF RIEMANNIAN FOLIATION
title_sort	on some infinitesimal automorphisms of riemannian foliation
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2007
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172007000100001
work_keys_str_mv	AT chaouchmohametali onsomeinfinitesimalautomorphismsofriemannianfoliation AT torkihamzanabila onsomeinfinitesimalautomorphismsofriemannianfoliation
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ON SOME INFINITESIMAL AUTOMORPHISMS OF RIEMANNIAN FOLIATION

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