Ianus, S.; Rizza, G. B. Totally umbilical submanifolds: some remarks. (English) Zbl 0935.53025 Riv. Mat. Univ. Parma, V. Ser. 6, 213-218 (1997). 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 Keywords:totally umbilic submanifolds; constant holomorphic curvature; constant sectional curvature; almost Hermitian manifolds PDFBibTeX XMLCite \textit{S. Ianus} and \textit{G. B. Rizza}, Riv. Mat. Univ. Parma, V. Ser. 6, 213--218 (1997; Zbl 0935.53025)