arXiv research

The study defines and analyzes semi-invariant submanifolds in complex contact metric manifolds.

In this paper, we study normal complex contact metric manifolds and we get some general results on them. Moreover, we obtained the general expression of the curvature tensor field for arbitrary vector fields. Furthermore, we show that the necessary and succient conditions to be normal a complex contact metric manifold.…

Study weak quasi contact metric manifolds to generalize K-contact and Sasakian manifolds criteria.

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

Paper finds previous work on submanifolds incorrect.

Study on Yamabe solitons on specific complex manifolds, focusing on torse-forming vector fields.

The paper connects complex contact structures to specific types of almost contact 3-structures.

We consider a pair of smooth manifolds, which are the counterparts in the even-dimensional and odd-dimensional cases. They are separately an almost complex manifold with Norden metric and an almost contact manifolds with B-metric, respectively. They can be combined as the so-called almost contact complex Riemannian man…

Sobolev mappings preserve the Rumin complex on contact manifolds.

Study on solitons in complex Riemannian manifolds with specific properties.

Study of Yamabe solitons on specific geometric manifolds.

New solitons defined for Sasaki-like almost contact complex Riemannian manifolds.

Study weak $f$-K-contact manifolds, finding Einstein-type metrics and solitons.

Study harmonicity of normal almost contact structures on Riemannian manifolds.

Study of contact-complex Riemannian submersions in various manifold classes.

The object of study in the present dissertation are some topics in differential geometry of smooth manifolds with additional tensor structures and metrics of Norden type. There are considered four cases depending on the dimension of the manifold: 2n, 2n + 1, 4n and 4n + 3. The studied tensor structures, which are count…

We construct several natural connections and Dirac type operators on a general metric contact manifold which are more sensitive to the geometric background. In the special case of CR manifolds these connections are also compatible with the CR structure and include among them the Webster connection. We also describe sev…

The object of investigations are almost contact B-metric manifolds which are derived as a product of a real line and a 2-dimensional manifold equipped with a complex structure and a Norden metric. There are used two different methods for generation of the B-metric on the product manifold. The constructed manifolds are …

The paper characterizes Sasakian manifolds using weak nearly Sasakian structures.

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 apply these general results to obtain classifications of contact hypersurfaces …

In this paper we obtain the structure equation of a contact-complex Riemannian submersion and give some applications of this equation in the study of almost cosymplectic manifolds with Kaehler fibres.

We give a characterization of a contact metric manifold as a special almost contact metric manifold and discuss an almost contact metric manifold which is {a} natural generalization of the contact metric manifolds introduced by Y. Tashiro.

The study explores new metric structures on manifolds, linking them to Einstein metrics.

Survey of recent results in weak almost contact structures.

Study on generalized quasi-Einstein structures in contact geometry.

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 Kähler-Einstein metric of positive scalar curvature, we show that it is the Salamon twistor space of a quaternion-Kähler man…

We study almost bi-paracontact structures on contact manifolds. We prove that if an almost bi-paracontact structure is defined on a contact manifold $(M,η)$, then under some natural assumptions of integrability, $M$ carries two transverse bi-Legendrian structures. Conversely, if two transverse bi-Legendrian structures …

Study on Ricci solitons and Einstein metrics in weak β-Kenmotsu manifolds.

The paper studies contact pseudo-metric manifolds with a specific curvature condition.

Unified framework for classifying Sasakian, K-contact, and (κ, μ)-manifolds.

Compact metric f-K-contact manifolds constructed via specific transformations.

Study on curvature properties of N(κ)-contact metric manifolds with generalized Tanaka-Webster connection.

The paper studies $η-$Ricci solitons on contact pseudo-metric manifolds and their properties.

The paper defines quasi-isometry for almost contact metric manifolds and explores its properties.

In this paper, we prove that evry 3-dimensional manifold M is a ?- recurrent N(k)-contact metric manifold if and only if it is flat. Then we classify the ?-recurrent contact metric manifolds of constant curvature. This implies that there exists no ?-recurrent N(k)-contact metric manifold, which is neither symmetric nor…

The paper studies a new structure on contact manifolds and its foliation properties.

The author is planning if possible classify all three-dimensional $(κ,μ)$-manifolds wether contact metric, almost cosymplectic, para-contact metric, almost para-cosymplectic. Of course classification in contact or almost cosymplectic cases already is provdied. Up to authors knowledge there is no classification for para…

In this article, we study an almost contact metric structure on a $G_2$-manifold constructed by Arikan, Cho and Salur in via the classification of almost contact metric structures given by Chinea and Gonzalez. In particular, we characterize when this almost contact metric structure is cosymplectic and narrow down the p…

The study explores $(m,ρ)$-quasi-Einstein structures on contact metric manifolds.

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 almost contact metric spaces, more precisely, Hermitian almost contact metric spac…

The paper studies special solitons on specific contact metric manifolds.

We discuss a correspondence between certain contact pairs on the one hand, and certain locally conformally symplectic forms on the other. In particular, we characterize these structures through suspensions of contactomorphisms. If the contact pair is endowed with a normal metric, then the corresponding lcs form is loca…

The paper classifies special types of contact metric manifolds with curvature conditions.

In this paper the geometry of normal metric contact pair manifolds is studied under the flatness of conformal, concircular and quasi-conformal curvature tensors. It is proved that a conformal flat normal metric contact pair manifold is an Einstein manifold with a negative scalar curvature and has positive sectional cur…

The paper classifies contact 3-manifolds with critical metrics and connects entropy to optimization.

Families of linear connections are constructed on almost contact manifolds with Norden metric. An analogous connection to the symmetric Yano connection is obtained on a normal almost contact manifold with Norden metric and closed structural 1-form. The curvature properties of this connection are studied on two basic cl…

It is introduced a differentiable manifold with almost contact 3-structure which consists of an almost contact metric structure and two almost contact B-metric structures. The product of this manifold and a real line is an almost hypercomplex manifold with Hermitian-Norden metrics. It is proven that the introduced mani…

Study new warped product metric in contact geometry.