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Annals of Global Analysis and Geometry

, Volume 37, Issue 3, pp 221–240 | Cite as

Decomposition and minimality of lagrangian submanifolds in nearly Kähler manifolds

  • Lars SchäferEmail author
  • Knut Smoczyk
Original Paper

Abstract

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.

Keywords

Lagrangian Nearly Kähler Minimal Twistor spaces Decomposition 

Mathematics Subject Classification (2000)

53C42 53C15 32Q60 

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Institut für DifferentialgeometrieLeibniz Universität HannoverHannoverGermany

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