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arXiv · 1310.0649

The constancy of principal curvatures of curvature-adapted submanifolds in symmetric spaces

Naoyuki Koike
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Abstract

In this paper, we investigate complete curvature-adapted submanifolds with maximal flat section and trivial normal holonomy group in symmetric spaces of compact type or non-compact type under certain condition, and derive the constancy of the principal curvatures of such submanifolds. As its result, we can derive that such submanifolds are isoparametric.

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Naoyuki Koike. 2014-06-18. The constancy of principal curvatures of curvature-adapted submanifolds in symmetric spaces. https://doi.org/10.1016/j.difgeo.2014.06.007

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