Related papers: Geometric realizations of affine Kaehler curvature…

We prove that any simply connected special Kaehler manifold admits a canonical immersion as a parabolic affine hypersphere. As an application, we associate a parabolic affine hypersphere to any nondegenerate holomorphic function. Also we…

We classify all Kahler metrics in an open subset of $C^2$ whose real geodesics are circles. All such metrics are equivalent (via complex projective transformations) to Fubini metrics (i.e. to Fubini-Study metric on $CP^2$ restricted to an…

We prove that any holomorphic geometric structure of affine type on an Oeljeklaus- Toma manifold is locally homogeneous. For locally conformal K\"ahler Oeljeklaus-Toma manifolds we prove that all holomorphic geometric structures, and also…

In order to understand the structure of the cohomologies involved in the study of projectively equivariant quantizations, we introduce a notion of affine representation of a Lie algebra.We show how it is related to linear representations…

We study the topology of complete Finsler manifolds admitting convex functions

We show that every closed symplectic four-dimensional manifold admits compatible almost Kaehler metrics of negative scalar curvature.

The following results are proved: Theorem 1. A totally real semiparallel submanifold of constant curvature with parallel f-structure in the normal bundle of a K\"ahler manifold N is flat or a totally geodesic submanifold of N. Theorem 2. A…

We present a simple geometric construction linking geometric to deformation quantization. Both theories depend on some apparently arbitrary parameters, most importantly a polarization and a symplectic connection, and for real polarizations…

Some curvature properties of Kahler manifolds of indefinite metrics are studied. Analogues of a Kulkarni's theorem are proved for such manifolds.

We show how to write any Kaehler metric of complex dimension 2 admitting a holomorphic isometry as a simple 1-real-function deformation of a Gibbons-Hawking metric. Hyper-Kaehler metrics with a tri-holomorphic isometry (Gibbons-Hawking…

We explicitly construct the algebraic model of affine Jacobian of a generic algebraic curve of high genus and use it to compute the Euler characteristic of the Jacobian and investigate its structure.

We present an explicit formula for the deformation quantization on K\"{a}hler manifolds.

Geometry is wavy: even at the purely geometric level (no particular theory chosen), curvature satisfies a covariant quasilinear wave equation. In Riemannian geometry equipped with the Levi-Civita connection, the Riemann curvature tensor…

The aim of this paper is to classify compact, simply connected K\"ahler manifolds which admit totally geodesic, holomorphic complex homothetic foliation by curves.

In this paper we prove that every Riemannian metric on a locally conformally flat manifold with umbilic boundary can be conformally deformed to a scalar flat metric having constant mean curvature. This result can be seen as a generalization…

We prove that an admissible manifold (as defined by Apostolov, Calderbank, Gauduchon and T{\o}nnesen-Friedman), arising from a base with a local K\"ahler product of constant scalar curvature metrics, admits Generalized Quasi-Einstein…

Every algebraic variety can be regarded as a symplectic manifold being equipped with a Kahler form. Therefore it is natural to study lagrangian geometry of any algebraic variety. We present two basic constructions which can be applied to a…

We present a geometric formulation of quantum mechanics based on the symplectic structure of the projective Hilbert space. Building upon the standard K\"ahler framework, we introduce an extension in which the symplectic structure is allowed…

We present the exact realization of the extended Snyder model. Using similarity transformations, we construct realizations of the original Snyder and the extended Snyder models. Finally, we present the exact new realization of the…

In this paper we generalize Drinfeld's twisted quantum affine algebras to construct twisted quantum algebras for all simply-laced generalized Cartan matrices and present their vertex representation realizations.