Related papers: Hypersurfaces of nearly Kahler twistor spaces

Each hypersurface of a nearly K\"ahler manifold is naturally equipped with two tensor fields of $(1,1)$-type, namely the shape operator $A$ and the induced almost contact structure $\phi$. In this paper, we show that, in the homogeneous NK…

In the context of six-dimensional homogeneous nearly K\"ahler manifolds, we prove that $\mathbb S^6$ is the only ambient space admitting constant sectional curvature hypersurfaces. In order to do so, we prove first that in $\mathbb…

For an almost contact metric manifold $N$, we find conditions for which either the total space of an $S^1$-bundle over $N$ or the Riemannian cone over $N$ admits a strong K\"ahler with torsion (SKT) structure. In this way we construct new…

We study hypersurfaces in a nearly $\mathrm{G}_2$ manifold. We define various quantities associated to such a hypersurface using the $\mathrm{G}_2$ structure of the ambient manifold and prove several relationships between them. In…

In this work, we prove that every complex contact structure gives rise to a distinguished type of almost contact metric 3-structure. As an application of our main result, we provide several new examples of manifolds which admit taut contact…

A contact hypersurface in a Kaehler manifold is a real hypersurface for which the induced almost contact metric structure determines a contact structure. We carry out a systematic study of contact hypersurfaces in Kaehler manifolds. We then…

This paper deals with a limiting case motivated by contact geometry. The limiting case of a tensorial characterization of contact hypersurfaces in Kahler manifolds leads to Hopf hypersurfaces whose maximal complex subbundle of the tangent…

We study and classify almost complex totally geodesic submanifolds of the nearly Kaehler flag manifold $F_{1,2}(\mathbb C^3)$, and of its semi-Riemannian counterpart. We also develop a structural approach to the nearly Kaehler flag manifold…

Let M be a six dimensional manifold, endowed with a cohomogeneity one action of G= SU_2 x SU_2, and M_reg its subset of regular points. We show that M_reg admits a smooth, 2-parameter family of G-invariant, non-isometric strict nearly…

We study pseudoholomorphic curves in the nearly Kalher $\mathbf{CP}^3$. It is shown that a class of curves called null-torsion are in one to one correspondence with the integrals of a holomorphic contact system on the usual Kahler…

In this paper, we construct complex metric structures on complex hypersurfaces in hyperkahler manifolds. This construction is that in contact geometry.

Let $(M,I)$ be an almost complex 6-manifold. The obstruction to integrability of almost complex structure (so-called Nijenhuis tensor) maps a 3-dimensional bundle to a 3-dimensional one. We say that Nijenhuis tensor is non-degenerate if it…

We study the space of (orthogonal) almost complex structures on closed six-dimensional manifolds as the space of sections of the twistor space for a given metric. For a connected six-manifold with vanishing first Betti number, we express…

In a previous paper, the authors together with L. Vrancken initiated the study of $3$-dimensional CR submanifolds of the nearly K\" ahler homogeneous $\mathbb S^3\times \mathbb S^3$. As is shown by Butruille this is one of only four…

We show that the almost complex structure underlying a non-Kahler, nearly Kahler 6-manifold (in particular, the standard almost complex structure of S^6) cannot be compatible with any symplectic form, even locally.

A hypercomplex manifold is by definition a smooth manifold equipped with two anticommuting integrable almost complex structures. For example, every hyperkaehler manifold is canonically hypercomplex (the converse is not true). For every…

We characterize HKT structure in terms of nondegenrate complex Poisson bivector on hypercomplex manifold. We extend the characterization to the twistor space. After considering the flat case in detail, we show that the twistor space of…

We establish the conditions for the induced generalized metric F structure of an oriented hypersurface of a generalized K\"ahler manifold to be a generalized CRFK structure. Then, we discuss a notion of generalized almost contact structure…

The structure of nearly K\"ahler manifolds was studied by Gray in several papers. More recently, a relevant progress on the subject has been done by Nagy. Among other results, he proved that a strict and complete nearly K\"ahler manifold is…

Let Z be a compact complex (2n+1)-manifold which carries a {\em complex contact structure}, meaning a codimension-1 holomorphic sub-bundle D of TZ which is maximally non-integrable. If Z admits a K\"ahler-Einstein metric of positive scalar…