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Totally umbilical submanifolds: some remarks. (English) Zbl 0935.53025

The present paper collects some results concerning totally umbilical submanifolds of Riemannian manifolds. We give a new characterization of totally umbilical submanifolds, and we consider Riemannian manifolds of constant sectional curvature and almost Hermitian manifolds of constant holomorphic, anti-holomorphic curvature and prove some results about the sectional curvature of their totally umbilical submanifolds.

MSC:

53C40 Global submanifolds
53C55 Global differential geometry of Hermitian and Kählerian manifolds
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