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Invariant submanifolds in flow geometry

Part of: Local differential geometry Global differential geometry

Published online by Cambridge University Press:  09 April 2009

J. C. González-Dávila ,
M. C. González-Dávila  and
L. Vanhecke
J. C. González-Dávila
Affiliation:
Department o de Matemática Fundamental Sección de Geometría y Topología Universidad de La LagunaLa Laguna, Spain
M. C. González-Dávila
Affiliation:
Department of Mathematics Katholieke Universiteit LeuvenCelestijnenlaan 200 B B-3001 Leuven, Belgium
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Abstract

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We begin a study of invariant isometric immersions into Riemannian manifolds (M, g) equipped with a Riemannian flow generated by a unit Killing vector field ξ. We focus our attention on those (M, g) where ξ is complete and such that the reflections with respect to the flow lines are global isometries (that is, (M, g) is a Killing-transversally symmetric space) and on the subclass of normal flow space forms. General results are derived and several examples are provided.

Keywords

Isometricnormal and contact flowsKilling-transversally symmetric spacesnormal fow space formsinvariant immersions and embeddings

MSC classification

Secondary: 53B25: Local submanifolds 53C12: Foliations (differential geometric aspects) 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.) 53C35: Symmetric spaces 53C40: Global submanifolds
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 62 , Issue 3 , June 1997 , pp. 290 - 314
Copyright
Copyright © Australian Mathematical Society 1997

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