In this paper we introduce harmonic Lagrangian submanifolds in general Kähler manifolds, which generalize special Lagrangian submanifolds in Calabi-Yau manifolds. We will use the deformation theory of harmonic Lagrangian submanifolds in Kähler manifolds to construct minimal Lagrangian torus in certain Kähler-Einstein manifolds with negative first Chern class.

In this paper, the geometry of F -invariant CR-submanifolds of a Kaehlerian product manifold is studied. Fundamental properties of this type submanifolds are investigated such as CR-product, D⊥-totally geodesic and mixed geodesic submanifold. Finally, we have researched totally-umbilical F -invariant proper CR-submanifolds and CR-products in a Kaehlerian product manifold M = M1(c1)×M2(c2) M.S.C...

H-minimal Lagrangian submanifolds in general Kähler manifolds generalize special Lagrangian submanifolds in Calabi-Yau manifolds. In this paper we will use the deformation theory of H-minimal Lagrangian submanifolds in Kähler manifolds to construct minimal Lagrangian torus in certain Kähler-Einstein manifolds with negative first Chern class.

Let \begin{document}$ (M,g) $\end{document} a compact Riemannian id="M2">\begin{document}$ n $\end{document}-dimensional manifold. It is well know that, under certain hypothesis, in the conformal class of id="M3">\begin{document}$ g there are scalar-flat metrics that have id="M...

In this paper, we study the geometry of half lightlike submanifolds of an indefinite Sasakian manifold. There are several different types of half lightlike submanifolds of an indefinite Sasakian manifold according to the form of its structure vector field. We study two types of them here: tangential and ascreen half lightlike submanifolds.

We construct symplectic submanifolds of symplectic manifolds with contact border. The boundary of such submanifolds is shown to be a contact submanifold of the contact border. We also give a topological characterization of the constructed submanifolds by means of a “relative Lefschetz hyperplane Theorem”. We sketch some of the applications of the results.