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

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

2008-12-22

arxiv.org/abs/0812.4256v4

'Complex and Differential Geometry', Springer Proceedings in Mathematics 8, (2011), 65--80

Mathematics

Differential Geometry

13 pages. Former title: 'Lagrangian mean curvature flow in almost K\"ahler-Einstein manifolds'

Scientific paper

We introduce the notion of K\"ahler 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 K\"ahler 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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