In the present note we study the existence or non-existence of doubly warped and doubly twisted product CR-submanifolds in nearly Kaehler manifolds.

In dimension greater than four, we prove that if a Hermitian non-Kaehler manifold is of pointwise constant antiholomorphic sectional curvatures, then it is of constant sectional curvatures.

The geometry of CR-submanifolds of Kaehler manifolds was initiated by Bejancu 1 and has been developed by 2–5 and others. They studied the geometry of CR-submanifolds with positive definite metric. Thus, this geometry may not be applicable to the other branches of mathematics and physics, where the metric is not necessarily definite. Moreover, because of growing importance of lightlike submanif...

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...

The first obstacle in building a Geometric Quantization theory for nilpotent orbits of a real semisimple Lie group has been the lack of an invariant polarization. In order to generalize the Fock space construction of the quantum mechanical oscillator, a polarization of the symplectic orbit invariant under the maximal compact subgroup is required. In this paper, we explain how such a polarizatio...

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 $M$ be an orientable hypersurface in the Euclidean space $R^{2n}$ with induced metric $g$ and $TM$ be its tangent bundle. It is known that the tangent bundle $TM$ has induced metric $overline{g}$ as submanifold of the Euclidean space $R^{4n}$ which is not a natural metric in the sense that the submersion $pi :(TM,overline{g})rightarrow (M,g)$ is not the Riemannian submersion. In this paper...