Generalized Lagrangian mean curvature flow in Kähler manifolds that are almost Einstein

Tapio Behrndt

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arXiv · 0812.4256

Generalized Lagrangian mean curvature flow in Kähler manifolds that are almost Einstein

Tapio Behrndt

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Abstract

We introduce the notion of Kähler manifolds that are almost Einstein and we define a generalized mean curvature vector field along submanifolds in them. We prove that Lagrangian submanifolds remain Lagrangian, when deformed in direction of the generalized mean curvature vector field. For a Kähler manifold that is almost Einstein, and which in addition has a trivial canonical bundle, we show that the generalized mean curvature vector field of a Lagrangian submanifold is the dual vector field associated to the Lagrangian angle.

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BibTeX RIS

Tapio Behrndt. 2011-07-15. Generalized Lagrangian mean curvature flow in Kähler manifolds that are almost Einstein. https://arxiv.org/abs/0812.4256

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