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Classification of isoparametric submanifolds admitting a reflective focal submanifold in symmetric spaces of non-compact type. (arXiv:1708.02773v3 [math.DG] UPDATED)

来源于:arXiv
In this paper, we study a full irreducible complete isoparametric submanifold of codimension greater than one in a symmetric space of non-compact type. First we prove that, if such an isoparametric submanifold admits a reflective focal submanifold, then it is curvature-adapted, where the ambient symmetric space may be of compact type. Next we prove that, if such an isoparametric submanifold admits a reflective focal submanifold and if it is of real analytic, then it is a principal orbit of a Hermann type action. 查看全文>>