Extrinsic homogeneity of parallel submanifolds |
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Authors: | Tillmann Jentsch |
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Affiliation: | 1. Fasanenstrasse 33, 51427, Bergisch Gladbach, Germany
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Abstract: | We consider parallel submanifolds M of a Riemannian symmetric space N and study the question whether M is extrinsically homogeneous in N, i.e. whether there exists a subgroup of the isometry group of N which acts transitively on M. Provided that N is of compact or non-compact type, we establish the extrinsic homogeneity of every complete irreducible parallel submanifold of N whose dimension is at least three and which is not contained in any flat of N. |
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