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On Curvature-Adapted and Proper Complex Equifocal Sub-manifolds
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  • Journal title : Kyungpook mathematical journal
  • Volume 50, Issue 4,  2010, pp.509-536
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2010.50.4.509
 Title & Authors
On Curvature-Adapted and Proper Complex Equifocal Sub-manifolds
Koike, Naoyuki;
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In this paper, we investigate curvature-adapted and proper complex equifocal submanifolds in a symmetric space of non-compact type. The class of these submanifolds contains principal orbits of Hermann type actions as homogeneous examples and is included by that of curvature-adapted and isoparametric submanifolds with flat section. First we introduce the notion of a focal point of non-Euclidean type on the ideal boundary for a submanifold in a Hadamard manifold and give the equivalent condition for a curvature-adapted and complex equifocal submanifold to be proper complex equifocal in terms of this notion. Next we show that the complex Coxeter group associated with a curvature-adapted and proper complex equifocal submanifold is the same type group as one associated with a principal orbit of a Hermann type action and evaluate from above the number of distinct principal curvatures of the submanifold.
proper complex equifocal submanifold;Hermann type action;complex Coxeter group;
 Cited by
The constancy of principal curvatures of curvature-adapted submanifolds in symmetric spaces, Differential Geometry and its Applications, 2014, 35, 103  crossref(new windwow)
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