Surfaces of nonpositive extrinsic curvature in spaces of constant curvature

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.
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