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Decomposition and minimality of lagrangian submanifolds in nearly Kähler manifolds


We show that Lagrangian submanifolds in six-dimensional nearly Kähler (non-Kähler) manifolds and in twistor spaces Z 4n+2 over quaternionic Kähler manifolds Q 4n are minimal. Moreover, we prove that any Lagrangian submanifold L in a nearly Kähler manifold M splits into a product of two Lagrangian submanifolds for which one factor is Lagrangian in the strict nearly Kähler part of M and the other factor is Lagrangian in the Kähler part of M. Using this splitting theorem, we then describe Lagrangian submanifolds in nearly Kähler manifolds of dimensions six, eight, and ten.

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Correspondence to Lars Schäfer.

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This article was written in the framework of the Graduiertenkolleg 1463 “Analysis, Geometry and String Theory”.

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Schäfer, L., Smoczyk, K. Decomposition and minimality of lagrangian submanifolds in nearly Kähler manifolds. Ann Glob Anal Geom 37, 221–240 (2010).

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  • Lagrangian
  • Nearly Kähler
  • Minimal
  • Twistor spaces
  • Decomposition

Mathematics Subject Classification (2000)

  • 53C42
  • 53C15
  • 32Q60