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Divergence-preserving geodesic transformations

Published online by Cambridge University Press:  14 November 2011

E. García-Río  and
L. Vanhecke
E. García-Río
Affiliation:
Facultade de Matemáticas, Universidade de Santiago de Compostela, 15706 Santiago de Compostela, Spain e-mail: [email protected]
L. Vanhecke
Affiliation:
Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, 3001 Leuven, Belgium e-mail: [email protected]
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Extract

We discuss divergence- and volume-preserving geodesic transformations with respect to submanifolds and in particular, with respect to hypersurfaces. We use these transformations to derive characterisations of special classes of hypersurfaces such as isoparametric hypersurfaces and Hopf hypersurfaces with constant principal curvatures. Furthermore, we consider divergence-preserving geodesic transformations with respect to geodesic spheres.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 6 , 1998 , pp. 1309 - 1323
Copyright
Copyright © Royal Society of Edinburgh 1998

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