Special isoparametric orbits in Riemannian symmetric spaces. (English) Zbl 0832.53042
The author treats principal orbits \(M\) of isotropy subgroups in Riemannian symmetric spaces of compact and non-compact type and shows that these \(M\) are isoparametric submanifolds. Further, he shows that, except in some special cases, the eigenspace distributions of the shape operator with respect to the radial unit vector field are involutive and their integral submanifolds are totally geodesic in \(M\). Finally, it is also shown that these isoparametric submanifolds are curvature-adapted submanifolds.
Reviewer: L.Vanhecke (Leuven)
Keywords:
principal orbits; isotropy subgroups; Riemannian symmetric spaces; isoparametric submanifolds; shape operatorReferences:
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