Broadly-Pluriminimal Submanifolds of Kaehler-Einstein Manifolds

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We define broadly-pluriminimal immersed 2n-submanifold F: M --> N into a Kaehler-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 no complex directions, then it is a Lagrangian submanifold, generalising the well-known case n = 1 for minimal surfaces due to Wolfson. We also prove that, if F has constant Kaehler 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 Kaehler angles.
17 pages, plain LaTeX

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Differential Geometry, 53A10, 53C42, 58E20, 53C55, 32C17, 53C15, 58F05

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http://salesiana.dossiersoluciones.com/handle/123456789/59025

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0004093
 http://arxiv.org/abs/math/0004093

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arXiv