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Let be a real submanifold of an almost complex manifold and let be the maximal holomorphic subspace, for each . We prove that , is upper-semicontinuous.
In this paper, we prove that the first eigenvalue of a complete spacelike submanifold in with the bounded Gauss map must be zero.
Let be an -dimensional submanifold in the unit sphere , we call a -extremal submanifold if it is a critical point of the functional . In this paper, we can study gap phenomenon for these submanifolds.
Let Mⁿ be a compact Landsberg hypersurface of a Minkowski space with constant mean curvature H. Using the Gauss formula for the Chern connection of Finsler submanifolds, we prove that if M is convex, then M is Riemannian with constant curvature.
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