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Israel Journal of Mathematics

, Volume 146, Issue 1, pp 223–242 | Cite as

A basic inequality and new characterization of Whitney spheres in a complex space form

  • Haizhong Li
  • Luc Vrancken
Article

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:\(\left| {\bar \nabla h} \right|^2 \geqslant \frac{{3n^2 }}{{n + 2}}\left| {\nabla ^ \bot \vec H} \right|^2 \) 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.

Keywords

Fundamental Form Curvature Vector Lagrangian Submanifold Complex Space Form Tangent Vector Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© The Hebrew University Magnes Press 2005

Authors and Affiliations

  1. 1.Department of Mathematical SciencesTsinghua UniversityBeijingPeople's Republic, of China
  2. 2.LAMATH, ISTV 2, Campus du Mont HouyUniversité de ValenciennesValenciennes Cedex 9France

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