Related papers: Contact hypersurfaces in Kaehler manifolds
A contact manifold is a manifold equipped with a distribution of codimension one that satisfies a `maximal non-integrability' condition. A standard example of a contact structure is a strictly pseudoconvex CR manifold, and operators of…
We introduce higher order mean curvatures of screen almost conformal (SAC) half-lightlike submanifolds of indefinite contact manifolds, admitting a semi-symmetric non-metric connection, and use them to generalize some known results of [6].…
We consider 5-manifolds with a contact form arising from a hypo structure, which we call \emph{hypo-contact}. We provide conditions which imply that there exists such a structure on an oriented hypersurface of a 6-manifold with a half-flat…
Let $M$ be a hyperkaehler manifold, and $F$ a torsion-free and reflexive coherent sheaf on $M$. Assume that $F$ (outside of its singularities) admits a connection with a curvature which is invariant under the standard SU(2)-action on…
In this paper the 5-dimensional contact SO(3)-manifolds are classified up to equivariant contactomorphisms. The construction of such manifolds with singular orbits requires the use of generalized Dehn twists. We show as an application that…
In this paper, homology of a contact CR-submanifold of a real hypersurface, which has naturally almost contact metric structure induced from the complex Euclidean space $\mathbb{C}^{m}$, is examined. More precisely, nonexistence of stable…
Hypersurfaces of manifolds of constant nonzero sectional curvature are classificated according their restricted homogeneous holonomy groups.
In this study, we investigate generalized quasi-Einstein structure for normal metric contact pair manifolds. Firstly, we deal with elementary properties and examine, existence, and characterizations of generalized quasi-Einstein normal…
We prove that under certain conditions on the mean curvature and on the Kaehler angles, a compact submanifold M of real dimension 2n, immersed into a Kaehler-Einstein manifold N of complex dimension 2n, must be either a complex or a…
In this paper, we give the geometric meaning of hypersurfaces with constant mean curvature in a Finsler manifold by using volume preserving variation. Then we give the correspondence between principal curvatures of submanifolds by a…
We study curvature identities on contact metric manifolds on the geometry of the corresponding almost K\"aehler cones, and we provide applications of the derived curvature identities.
We give some classifications of biharmonic hypersurfaces with constant scalar curvature. These include biharmonic Einstein hypersurfaces in space forms, compact biharmonic hypersurfaces with constant scalar curvature in a sphere, and some…
In this article we introduce and analyze in detail singular contact structures, with an emphasis on $b^m$-contact structures, which are tangent to a given smooth hypersurface $Z$ and satisfy certain transversality conditions. These singular…
We study the K\"ahler geometry of stage n Bott manifolds, which can be viewed as $n$-dimensional generalizations of Hirzebruch surfaces. We show, using a simple induction argument and the generalized Calabi construction from…
We classify all real hypersurfaces with three distinct constant principal curvatures in complex hyperbolic spaces of dimension greater than two.
In this paper, we study hypersurfaces in $\mathbb{H}^2\times\mathbb{H}^2$. We first classify the hypersurfaces with constant principal curvatures and constant product angle function. Then, we classify homogeneous hypersurfaces and…
We present new constructions of Kaehler metrics with constant scalar curvature on complex surfaces, in particular on certain del Pezzo surfaces. Some higher dimensional examples are provided as well.
We study geometry, topology and deformation spaces of noncompact complex hyperbolic manifolds (geometrically finite, with variable negative curvature), whose properties make them surprisingly different from real hyperbolic manifolds with…
A taut contact sphere on a 3-manifold is a linear 2-sphere of contact forms, all defining the same volume form. In the present paper we completely determine the moduli of taut contact spheres on compact left-quotients of SU(2) (the only…
In this paper, we introduce two notions on a surface in a contact manifold. The first one is called degree of transversality (DOT) which measures the transversality between the tangent spaces of a surface and the contact planes. The second…