Related papers: On contact pseudo-metric manifolds satisfying a nu…

The present note deals with the properties of metric connections $\nabla$ with vectorial torsion $V$ on semi-Riemannian manifolds $(M^n,g)$. We show that the $\nabla$-curvature is symmetric if and only if $V^{\flat}$ is closed, and that…

In this paper, we show that any compact K$\"a$hler manifold homotopic to a compact Riemannian manifold with negative sectional curvature admits a K$\"a$hler-Einstein metric of general type. Moreover, we prove that, on a compact symplectic…

In this paper, we show that there is no phi-recurrent Sasakian manifold. Then we prove that the only flat 3-dimensional manifolds are phi-recurrent (k, m)-contact metric manifolds.

We find some curvature properties of 3-quasi-Sasakian manifolds which are similar to some well-known identities holding in the Sasakian case. As an application, we prove that any 3-quasi-Sasakian manifold of constant horizontal sectional…

This paper applies the Newman-Penrose formalism-a technique primarily used in General Relativity-to the analysis of three-dimensional almost contact metric (ACM) manifolds. We reformulate and discuss several known notions and properties…

In this paper, we establish a "pseudo-effective" version of the holonomy principle for compact K\"{a}hler manifolds with nonnegative holomorphic sectional curvature. As applications, we prove that if a compact complex manifold $M$ admits a…

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…

In this paper, we study a general almost Schur Lemma on pseudo-Hermitian (2n+1)-manifolds $(M,J,\theta)$ for $n\geq2$. When the equality of almost Schur inequality holds, we derive the contact form $\theta$ is pseudo-Einstein and the…

We study the problem of deforming a Riemannian metric to a conformal one with nonzero constant scalar curvature and nonzero constant boundary mean curvature on a compact manifold of dimension $n\geq 3$. We prove the existence of such…

In this paper, we present the invalidities of the results in [3], because of their definition of a semi-invariant submanifold of an almost complex contact metric manifold is not true .

A contact manifold $M$ can be defined as a quotient of a symplectic manifold $X$ by a proper, free action of $\R^{>0}$, with the symplectic form homogeneous of degree 2. If $X$ is, in addition, Kaehler, and its metric is also homogeneous of…

An old conjecture in non-K\"ahler geometry states that, if a compact Hermitian manifold has constant holomorphic sectional curvature, then the metric must be K\"ahler (when the constant is non-zero) or Chern flat (when the constant is…

We classify the contact metric 3-manifolds that satisfy ||grad{\lambda}||=1 and \nabla_{{\xi}}{\tau}=2a{\tau}{\phi}.

We consider manifolds endowed with metric contact pairs for which the two characteristic foliations are orthogonal. We give some properties of the curvature tensor and in particular a formula for the Ricci curvature in the direction of the…

The flag curvature is a natural extension of the sectional curvature in Riemannian geometry, and the S-curvature is a non-Riemannian quantity which vanishes for Riemannian metrics. There are (incomplete) non-Riemannian Finsler metrics on an…

For each contact diffeomorphism $\phi: (Q,\xi) \to (Q,\xi)$ of $(Q,\xi)$, we equip its mapping torus $M_\phi$ with a \emph{locally conformal symplectic} form of Banyaga's type, which we call the \emph{$\text{\rm lcs}$ mapping torus} of…

All the connections, pure toward the nilpotent structure, are found. Examples of manifolds, for which the curvature tensor is pure or hybrid, are given. For a manifold of B-type a necessary and sufficient condition for purity of the…

We introduce two classes of null hypersurfaces of an indefinite Sasakian manifold, $(\overline{M}, \overline{\phi},\zeta, \eta)$, tangent to the characteristic vector field $\zeta$, called; {\it contact screen conformal} and {\it contact…

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.

In the present paper, we study globally framed f-manifolds in the particular setting of indefinite S-manifolds for both spacelike and timelike cases. We prove that if $M = N^{\perp} \times_f N^T$ is a warped CR-submanifold such that…