Related papers: A classification of certain almost $\alpha$-Kenmot…

We use a natural affine connection with nontrivial torsion on an arbitrary almost-Kaehler manifold which respects the almost-Kaehler structure to construct a Fedosov-type deformation quantization on this manifold.

We consider 6-dimensional strict nearly Kaehler manifolds acted on by a compact, cohomogeneity one automorphism group G. We classify the compact manifolds of this class up to G-diffeomorphisms. We also prove that the manifold has constant…

In the first part of this note we study compact Riemannian manifolds (M,g) whose Riemannian product with R is conformally Einstein. We then consider compact 6--dimensional almost Hermitian manifolds of type W_1+W_4 in the Gray--Hervella…

A $Q$-manifold $M$ is a supermanifold endowed with an odd vector field $Q$ squaring to zero. The Lie derivative $L_Q$ along $Q$ makes the algebra of smooth tensor fields on $M$ into a differential algebra. In this paper, we define and study…

We study the space of closed anti-invariant forms on an almost complex manifold, possibly non compact. We construct families of (non integrable) almost complex structures on $\R^4$, such that the space of closed $J$-anti-invariant forms is…

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…

This paper determined the components of the generalized curvature tensor for the class of Kenmotsu type and established the mentioned class is {\eta}-Einstein manifold when the generalized curvature tensor is flat; the converse holds true…

In the paper we develop a framework for the alternative way of the study of a local geometry of almost cosymplectic manifolds with Kahlerian leaves. The main idea is to apply the concept of a geometry and analysis of CR manifolds. Locally…

In this article, we study and analyze the \phi-sectional curvature induced by a statistical structure on an almost contact metric manifold. We demonstrate that this sectional curvature is always non-positive. Additionally, we present…

New relations involving curvature components for the various connections appearing in the theory of almost product manifolds are given and the conformal behaviour of these connections are studied. New identities for the irreducible parts of…

In this article, we characterize the distortion elements of the group of smooth diffeomorphisms of the circle and of the group of compactly supported smooth diffeomorphisms of the real line. More precisely, we prove that, in this context,…

This article reveals a significant connection in geometry: when the Lee form $\theta$ is normal to an almost Hermitian manifold $N$, it implies that $N$ possesses a nearly K\"ahler structure. Investigating locally conformally Spin(7)…

Many authors have studied Ricci solitons and their analogs within the framework of (almost) contact geometry. In this article, we thoroughly study the $(m,\rho)$-quasi-Einstein structure on a contact metric manifold. First, we prove that if…

The aim of the present paper is to study the properties of Kenmotsu manifolds equipped with a non-symmetric non-metric connection. We also establish some curvature properties of Kenmotsu manifolds. It is proved that a Kenmotsu manifold…

A simple Almost-Riemannian Structure on a Lie group G is defined by a linear vector field (that is an infinitesimal automorphism) and dim(G) -- 1 left-invariant ones. It is first proven that two different ARSs are isometric if and only if…

This paper is devoted to a systematic study and classification of invariant affine or metric connections on certain classes of naturally reductive spaces. For any non-symmetric, effective, strongly isotropy irreducible homogeneous…

In complex geometry a classical and useful invariant of a complex manifold is its Kodaira dimension. Since its introduction by Iitaka in the early 70's, its behavior under deformations was object of study and it is known that Kodaira…

We prove that the deformation space $AH(M)$ of marked hyperbolic 3-manifolds homotopy equivalent to a fixed compact 3-manifold $M$ with incompressible boundary is locally connected at quasiconformally rigid points.

In the first part of this series of papers we developed the invariant differentiation with respect to a Cartan connection, we described this procedure in the terms of the underlying principal connections, and we discussed applications of…

Following T.-J. Li, W. Zhang [Comparing tamed and compatible symplectic cones and cohomological properties of almost complex manifolds, Comm. Anal. Geom.], we continue to study the link between the cohomology of an almost-complex manifold…