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. © Springer-Verlag Berlin Heidelberg 2011.
CITATION STYLE
Behrndt, T. (2011). Generalized Lagrangian mean curvature flow in Kähler manifolds that are almost Einstein. Springer Proceedings in Mathematics, 8, 65–79. https://doi.org/10.1007/978-3-642-20300-8_3
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