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Decomposition and minimality of Lagrangian submanifolds in nearly K\"ahler manifolds

Authors
  • Schäfer, Lars
  • Smoczyk, Knut
Type
Preprint
Publication Date
Apr 23, 2009
Submission Date
Apr 23, 2009
Identifiers
arXiv ID: 0904.3683
Source
arXiv
License
Yellow
External links

Abstract

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

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