We verify the extension to zero section of momentum construction Kaehler-Einstein metrics and Kaehler-Ricci solitons on total space Y positive rational powers canonical line bundle toric Fano manifolds with possibly irregular Sasaki-Einstein metrics. More precisely, we show that extended metric along has an expression which can be Y, restricts associated unit circle as a transversely (Sasakian ...

Let (M, g, J) be a compact Hermitian manifold with a smooth boundary. Let ∆p,B and ⊓ ⊔p,B be the realizations of the real and complex Laplacians on p forms with either Dirichlet or Neumann boundary conditions. We generalize previous results in the closed setting to show that (M, g, J) is Kaehler if and only if Spec(∆p,B) = Spec(2 ⊓ ⊔p,B) for p = 0, 1. We also give a characterization of manifold...

In this paper, we introduce the new notion of quasi bi-slant submanifolds almost Hermitian manifolds. Necessary and sufficient conditions for integrability distributions which are involved in definition such a Kaehler manifold obtained. We also investigate necessary these manifolds to be totally geodesic study geometry foliations determined by above distributions. Finally, obtain submanifold lo...

A simply connected compact Kaehler manifold X is an irreducible symplectic manifold if there is an everywhere non-degenerate holomorphic 2-form Ω on X with H0(X,Ω2X) = C[Ω]. By definition, X has even complex dimension. There is a canonical symmetric form qX on H (X,Z), which is called the Beauville-Bogomolov form (cf. [Be]). On the other hands, since X is Kaehler, H(X,Z) has a natural Hodge str...