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The gap theorems for some extremal submanifolds in a unit sphere

Xi Guo and Lan Wu (2015)

Communications in Mathematics

Let M be an n -dimensional submanifold in the unit sphere S n + p , we call M a k -extremal submanifold if it is a critical point of the functional M ρ 2 k d v . In this paper, we can study gap phenomenon for these submanifolds.

The rigidity theorem for Landsberg hypersurfaces of a Minkowski space

Jin Tang Li (2012)

Annales Polonici Mathematici

Let Mⁿ be a compact Landsberg hypersurface of a Minkowski space ( V n + 1 , F ̅ ) 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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