A basic inequality and new characterization of Whitney spheres in a complex space form |
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Authors: | Email author" target="_blank">Haizhong?LiEmail author Luc?Vrancken |
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Institution: | (1) Department of Mathematical Sciences, Tsinghua University, 100084 Beijing, People's Republic, of China;(2) LAMATH, ISTV 2, Campus du Mont Houy, Université de Valenciennes, 59313 Valenciennes Cedex 9, France |
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Abstract: | LetN
n
(4c) be ann-dimensional complex space form of constant holomorphic sectional curvature 4c and letx:M
n
→N
n
(4c) be ann-dimensional Lagrangian submanifold inN
n
(4c). We prove that the following inequality always hold onM
n:
whereh is the second fundamental form andH is the mean curvature of the submanifold. We classify all submanifolds which at every point realize the equality in the above
inequality. As a direct consequence of our Theorem, we give, a new characterization of theWhitney spheres in a complex space form.
Partially supported by a research fellowship of the Alexander von Humboldt Stiftung. |
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Keywords: | |
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