Related papers: Torsion in almost Kaehler geometry

For G_2-manifolds the Fern\'andez-Gray class X_1+X_4 is shown to consist of the union of the class X_4 of G_2-manifolds locally conformal to parallel G_2-structures and that of conformal transformations of nearly parallel or weak holonomy…

In this article, we propose the following conjecture: if the Strominger connection of a compact Hermitian manifold has constant non-zero holomorphic sectional curvature, then the Hermitian metric must be K\"ahler. The main result of this…

We study the conditions under which an almost Hermitian structure $(G,J)$ of general natural lift type on the cotangent bundle $T^*M$ of a Riemannian manifold $(M,g)$ is K\" ahlerian. First, we obtain the algebraic conditions under which…

The geometry arising from Michelson & Strominger's study of N=4B supersymmetric quantum mechanics with superconformal D(2,1;alpha)-symmetry is a hyperKaehler manifold with torsion (HKT) together with a special homothety. It is shown that…

An almost K\"ahler structure is {\it extremal} if the Hermitian scalar curvature is a Killing potential [29]. When the almost complex structure is integrable it coincides with extremal K\"ahler metric in the sense of Calabi [8]. We observe…

We investigate the geometry of a twisting non-shearing congruence of null geodesics on a conformal manifold of even dimension greater than four and Lorentzian signature. We give a necessary and sufficient condition on the Weyl tensor for…

Let M be an almost Hermitian manifold of dimension greater or equal to 6. The following theorems are proved: Theorem 1. If M is of pointwise constant {\theta}-holomorphic sectional curvature for a number {\theta} in (0,{\pi}/2) then M is of…

We study the integrability to second order of infinitesimal Einstein deformations on compact Riemannian and in particular on K\"ahler manifolds. We find a new way of expressing the necessary and sufficient condition for integrability to…

Reflection in a line in Euclidean 3-space defines an almost paracomplex structure on the space of all oriented lines, isometric with respect to the canonical neutral Kaehler metric. Beyond Euclidean 3-space, the space of oriented geodesics…

In this paper we provide a \emph{global} investigation of the geometry of parallelizable manifolds (or absolute parallelism geometry) frequently used for application. We discuss the different linear connections and curvature tensors from a…

A Cartan manifold is a smooth manifold M whose slit cotangent bundle T*M0 is endowed with a regular Hamiltonian K which is positively homogeneous of degree 2 in momenta. The Hamiltonian K defines a (pseudo)-Riemannian metric gij in the…

In [SW2], we defined a generalized mean curvature vector field on any almost Lagrangian submanifold with respect to a torsion connection on an almost K\"ahler manifold. The short time existence of the corresponding parabolic flow was…

Using an integral identity proved by Sekigawa \cite{Sek87} on compact almost Hermitian 4-manifolds, we naturally obtain a global characterization of the class $\mathcal{AH}_1$ of almost Hermitian 4-manifolds satisfying the first Gray…

The Kaehler manifolds of quasi-constant holomorphic sectional curvatures are introduced as Kaehler manifolds with complex distribution of codimension two, whose holomorphic sectional curvature only depends on the corresponding point and the…

We introduce the notion of even Clifford structures on Riemannian manifolds, a framework generalizing almost Hermitian and quaternion-Hermitian geometries. We give the complete classification of manifolds carrying parallel even Clifford…

We establish a one-to-one correspondence between K\"ahler metrics in a given conformal class and parallel sections of a certain vector bundle with conformally invariant connection, where the parallel sections satisfy a set of non--linear…

This paper is a survey of results obtained by the authors on the geometry of connections with totally skew-symmetric torsion on the following manifolds: almost complex manifolds with Norden metric, almost contact manifolds with B-metric and…

We investigate a class of locally conformal almost K\"ahler structures and prove that, under some conditions, this class is a subclass of almost K\"ahler structures. We show that a locally conformal almost K\"ahler manifold admits a…

Almost contact structures can be identified with sections of a twistor bundle and this allows to define their harmonicity, as sections or maps. We consider the class of nearly cosymplectic almost contact structures on a Riemannian manifold…

We study an odd-dimensional analogue of the Goldberg conjecture for compact Einstein almost K\"ahler manifolds. We give an explicit non-compact example of an Einstein almost cok\"ahler manifold that is not cok\"ahler. We prove that compact…