• Kyungpook Mathematical Journal
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• 제50권4호
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• pp.509-536
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• 2010

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.