Geodesic
Surfaces of nonpositive extrinsic curvature in spaces of constant curvature
Sbornik. Mathematics, Tome 42 (1982) no. 3, pp. 297-310

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This paper investigates surfaces of nonpositive extrinsic curvature in a pseudo-Riemannian space $S^{l+p}_{l,p}$ of curvature 1, Kählerian submanifolds of complex projective space $P^n$, and saddle surfaces in spherical space $S^3$. It is determined under what conditions a surface is a totally geodesic submanifold. Bibliography: 14 titles. 
@article{SM_1982_42_3_a0,
     author = {A. A. Borisenko},
     title = {Surfaces of nonpositive extrinsic curvature in spaces of constant curvature},
     journal = {Sbornik. Mathematics},
     pages = {297--310},
     publisher = {mathdoc},
     volume = {42},
     number = {3},
     year = {1982},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1982_42_3_a0/}
}
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A. A. Borisenko. Surfaces of nonpositive extrinsic curvature in spaces of constant curvature. Sbornik. Mathematics, Tome 42 (1982) no. 3, pp. 297-310. http://geodesic.mathdoc.fr/item/SM_1982_42_3_a0/