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arXiv · 0904.3683

Decomposition and minimality of Lagrangian submanifolds in nearly Kähler manifolds

Lars Schäfer·Knut Smoczyk
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Abstract

We show that Lagrangian submanifolds in six-dimensional nearly Kähler (non Kähler) manifolds and in twistor spaces $Z\sp{4n+2}$ over quaternionic Kähler manifolds $Q\sp{4n}$ are minimal. Moreover, we will 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 second 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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Lars Schäfer, Knut Smoczyk. 2009-04-23. Decomposition and minimality of Lagrangian submanifolds in nearly Kähler manifolds. https://arxiv.org/abs/0904.3683

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