BROADLY-PLURIMINIMAL SUBMANIFOLDS OF KAHLER-EINSTEIN MANIFOLDS
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概要
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"We define broadly-pluriminimal immersed 2n-submanifold ＄ F:M￥rightarrow＄ ＄N＄ into a Kahler-Einstein manifold of complex dimension ＄2n＄ and scalar curvature ＄R＄. We prove that, if ＄M＄ is compact, ＄n￥geq 2＄ , and ＄R<0＄, then: (i) Either ＄F＄ has complex or Lagrangian directions; (ii) If ＄n=2,＄ ＄M＄ is oriented, and ＄F＄ has nocomplex directions, then it is a Lagrangian submanifold, generalizing the well-known case ＄n=1＄ for minimal surfaces due to Wolfgon. We also prove that, if ＄F＄ has constant Kahler angles with no complex directions, and is not Lagrangian, then ＄R=0＄ must hold. Our main tool is a formula on the Laplacian of a symmetric function on the Kahler angles."
- Yokohama City University and Yokohama National Universityの論文
- 2001-00-00
Yokohama City University and Yokohama National University | 論文
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