Related papers: Homology of contact CR-submanifolds

We classify the normal CR structures on $S^3$ and their automorphism groups. Together with [3], this closes the classification of normal CR structures on contact 3-manifolds. We give a criterion to compare 2 normal CR structures, and we…

We study harmonic almost contact structures in the context of contact metric manifolds, and an analysis is carried out when such a manifold fibres over an almost Hermitian manifold, as exemplified by the Boothby-Wang fibration. Two types of…

This research article introduces the concept of lightlike submanifolds of an indefinite Kenmotsu statistical manifold. Various results on geometry of contact CR and SCR-lightlike submanifolds have been developed. Some characterization…

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…

It is proved that a germ of a real analytic CR map from a smooth real-analytic minimal CR manifold M to an essentially finite real-algebraic generic submanifold M' of P^N of the same CR-dimension extends as a holomorphic correspondence…

We classify contact manifolds $(M,\mathcal D)$ which are homogeneous under a connected semisimple Lie group $G$, and symmetric in the sense that there exists a contactomorphism of $(M,\mathcal D)$ normalizing $G$, fixing a point $o$ in $M$…

A classification scheme of the conformal almost contact metric manifolds with respect to the covariant derivative of the Lee form is given. The subclasses of one basic class and their exact characterizations by the maximal subgroups of the…

We define generalized currents associated with immersions of abstract oriented solenoids with a transversal measure. We realize geometrically the full real homology of a compact manifold with these generalized currents, and more precisely…

In this paper the notion of the intrinsic geometry of an almost contact metric manifold is introduced. Description of some classes of spaces with almost contact metric structures in terms of the intrinsic geometry is given. A new type of…

For a compact almost complex 4-manifold $(M,J)$, we study the subgroups $H^{\pm}_J$ of $H^2(M, \mathbb{R})$ consisting of cohomology classes representable by $J$-invariant, respectively, $J$-anti-invariant 2-forms. If $b^+ =1$, we show that…

We say that a CR singular submanifold $M$ has a removable CR singularity if the CR structure at the CR points of $M$ extends through the singularity as an abstract CR structure on $M$. We study such real-analytic submanifolds, in which case…

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…

A rigorous foundation for the contact homology of Legendrian submanifolds in a contact manifold of the form $P\times \R$ where $P$ is an exact symplectic manifold is established. The class of such contact manifolds include 1-jet spaces of…

An almost para-CR structure on a manifold $M$ is given by a distribution $HM \subset TM$ together with a field $K \in \Gamma({\rm End}(HM))$ of involutive endomorphisms of $HM$. If $K$ satisfies an integrability condition, then $(HM,K)$ is…

We completely describe inhomogeneous properly embedded almost symmetric submanifolds of Euclidean space as certain unions of parallel symmetric submanifolds of the ambient Euclidean space.

We study the normal holonomy group, i.e. the holonomy group of the normal connection, of a CR-submanifold of a complex space form. We complete the local classification of normal holonomies for complex submanifolds. We show that the normal…

We study isoparametric hypersurfaces, whose principal curvatures are all constant, in the pseudo-Riemannian space forms. In this paper, we investigate two topics. Firstly, according to representations of Clifford algebras, we give a…

We give a loop group formulation for the problem of isometric immersions with flat normal bundle of a simply connected pseudo-Riemannian manifold $M_{c,r}^m$, of dimension $m$, constant sectional curvature $c \neq 0$, and signature $r$,…

This paper studies the geometric properties of contact CR-submanifolds of Sasakian statistical manifold. The integrability of invariant and anti-invariant distributions of contact CR-submanifolds has been characterized. Results on D-totally…

We define naturally Hermite-Lorentz metrics on almost-complex manifolds as special case of pseudo-Riemannian metrics compatible with the almost complex structure. We study their isometry groups.