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Every totally umbilical proper slant submanifold of a Kähler manifold is totally geodesic. (English) Zbl 1178.53056
Summary: We prove that there do not exist totally umbilical proper slant submanifolds in Kähler manifolds other than totally geodesic proper slant submanifolds.

MSC:
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
53C55 Global differential geometry of Hermitian and Kählerian manifolds
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