Lagrangian submanifolds in the 6-dimensional nearly Kähler manifolds with parallel second fundamental form

On Submanifolds with Tamed Second Fundamental Form

Based on the ideas of Bessa-Jorge-Montenegro [4] we show that a complete submanifold M with tamed second fundamental form in a complete Riemannian manifold N with sectional curvature KN ≤ κ ≤ 0 are proper, (compact if N is compact). In addition, if N is Hadamard then M has finite topology. We also show that the fundamental tone is an obstruction for a Riemannian manifold to be realized as subma...

Lagrangian Submanifolds in Hyperkähler Manifolds, Legendre Transformation

We develop the foundation of the complex symplectic geometry of Lagrangian subvarieties in a hyperkähler manifold. We establish a characterization, a Chern number inequality, topological and geometrical properties of Lagrangian submanifolds. We discuss a category of Lagrangian subvarieties and its relationship with the theory of Lagrangian intersection. We also introduce and study extensively a...

Lagrangian Submanifolds in Hyperkähler manifolds, Legendre transformation

Generic Submanifolds of Nearly Kaehler Manifolds with Certain Parallel Canonical Structure

The class of generic submanifold includes all real hypersurfaces, complex submanifolds, totally real submanifolds, and CR-submanifolds. In this paper we initiate the study of generic submanifolds in a nearly Kaehler manifold from differential geometric point of view. Some fundamental results in this paper will be obtained.

5 J ul 1 99 6 ON HYPER KÄHLER MANIFOLDS ASSOCIATED TO LAGRANGEAN KÄHLER SUBMANIFOLDS OF T

For any Lagrangean Kähler submanifold M ⊂ T Cn, there exists a canonical hyper Kähler metric on T ∗M . A Kähler potential for this metric is given by the generalized Calabi Ansatz of the theoretical physicists Cecotti, Ferrara and Girardello. This correspondence provides a method for the construction of (pseudo) hyper Kähler manifolds with large automorphism group. Using it, a class of pseudo h...