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Search: All articles in the CJM digital archive with keyword totally umbilic

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1. CJM 2009 (vol 61 pp. 641)

Maeda, Sadahiro; Udagawa, Seiichi
 Characterization of Parallel Isometric Immersions of Space Forms into Space Forms in the Class of Isotropic Immersions For an isotropic submanifold \$M^n\,(n\geqq3)\$ of a space form \$\widetilde{M}^{n+p}(c)\$ of constant sectional curvature \$c\$, we show that if the mean curvature vector of \$M^n\$ is parallel and the sectional curvature \$K\$ of \$M^n\$ satisfies some inequality, then the second fundamental form of \$M^n\$ in \$\widetilde{M}^{n+p}\$ is parallel and our manifold \$M^n\$ is a space form. Keywords:space forms, parallel isometric immersions, isotropic immersions, totally umbilic, Veronese manifolds, sectional curvatures, parallel mean curvature vectorCategories:53C40, 53C42

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