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Invariant submanifolds in flow geometry

Published online by Cambridge University Press:  09 April 2009

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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1997

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