Related papers: Indefinite locally conformal Kaehler manifolds

We give a partial account of some problems concerning cohomological invariants and metric properties of complex non-K\"ahler manifolds.

We define Cayley structures as a field of Cayley's ruled cubic surfaces over a four dimensional manifold and motivate their study by showing their similarity to indefinite conformal structures and their link to differential equations. In…

We give an up-to-date overview of geometric and topological properties of cosymplectic and coKaehler manifolds. We also mention some of their applications to time-dependent mechanics.

We introduce the notion of unbounded locally solid Riesz spaces, and investigate its fundamental properties.

We obtain a local classification of complex homothetic foliations on Kaehler manifolds by complex curves. This is used to construct almost Kaehler, Ricci-flat metrics subject to additional curvature properties.

We study unparametrized conformal circles, or called conformal geodesics, study diffeomorphisms mapping conformal circles to conformal circles in pseudo-Riemannian conformal manifolds. We show that such local diffeomorphisms are conformal…

A local classification of the Hermitian manifolds with flat associated connection is given. Hermitian manifolds admitting locally a conformal metric with flat associated connection are characterized by a curvature identity. Locally…

A locally conformally Kahler (LCK) manifold is a complex manifold admitting a Kahler covering M, such that its monodromy acts on this covering by homotheties. A compact LCK manifold is called LCK with potential if M admits an authomorphic…

We consider locally conformal Kaehler geometry as an equivariant, homothetic Kaehler geometry (K,\Gamma). We show that the de Rham class of the Lee form can be naturally identified with the homomorphism projecting \Gamma to its dilation…

An LCK (locally conformally Kahler) manifold is a complex manifold admitting a Kahler covering with monodromy acting by homotheties. Hopf manifolds and their submanifolds are the prime examples. This book presents an introduction to the…

The properties of Kaehler submanifolds with recurrent the second fundamental form in spaces of constant holomorphic sectional curvature are being studied in this article.

Motivated by analogous results in locally conformal symplectic geometry, we study different classes of G$_2$-structures defined by a locally conformal closed 3-form. In particular, we give a complete characterization of invariant exact…

In this thesis, we study cohomological properties of non-K\"ahler manifolds. In particular, we are concerned in investigating the cohomology of compact (almost-)complex manifolds, and of manifolds endowed with special structures, e.g.,…

In Kaehler manifolds are investigated conformally flat totally real submanifolds, which are semiparallel or have semiparallel mean curvature vector.

A locally conformally K\"ahler (LCK) manifold $M$ is one which is covered by a K\"ahler manifold $\tilde M$ with the deck transform group acting conformally on $\tilde M$. If $M$ admits a holomorphic flow, acting on $\tilde M$ conformally,…

A manifold $M$ is locally conformally Kahler (LCK) if it admits a Kahler covering with monodromy acting by holomorphic homotheties. Let $M$ be an LCK manifold admitting a holomorphic conformal flow of diffeomorphisms, lifted to a…

Let F be a K\"ahler foliation on a compact Riemannian manifold M. we study the properties of infinitesimal automorphisms on (M,F), and in particular we concentrate on the transversal conformal field, transversal projective field and…

We propose an approach to the existence problem for locally conformally K\"ahler metrics on compact complex manifolds by introducing and studying a functional that is different according to whether the complex dimension of the manifold is…

Through the study of some elliptic and parabolic fully nonlinear PDEs, we establish conformal versions of quermassintegral inequality, the Sobolev inequality and the Moser-Trudinger inequality for the geometric quantities associated to the…

We prove several results on the structure of solvable quotients of fundamental groups of compact Kahler manifolds (Kahler groups).