Geodesic
Characterization of Parallel Isometric Immersions of Space Forms into Space Forms in the Class of Isotropic Immersions
Canadian journal of mathematics, Tome 61 (2009) no. 3, pp. 641-655

Voir la notice de l'article provenant de la source Cambridge University Press

For an isotropic submanifold ${{M}^{n}}(n\underline{\underline{>}}3)$ of a space form ${{\tilde{M}}^{n+p}}(c)$ 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 ${{\tilde{M}}^{n+p}}$ is parallel and our manifold ${{M}^{n}}$ is a space form.
DOI : 10.4153/CJM-2009-034-4
Mots-clés : 53C40, 53C42, space forms, parallel isometric immersions, isotropic immersions, totally umbilic, Veronese manifolds, sectional curvatures, parallel mean curvature vector 
Maeda, Sadahiro; Udagawa, Seiichi. Characterization of Parallel Isometric Immersions of Space Forms into Space Forms in the Class of Isotropic Immersions. Canadian journal of mathematics, Tome 61 (2009) no. 3, pp. 641-655. doi: 10.4153/CJM-2009-034-4
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