Related papers: Generalised K\"ahler Structure on $\mathbb{C}P^2$ …

We present some fundamental facts about a class of generalized K\"ahler structures defined by invariant complex structures on compact Lie groups. The main computational tool is the BH-to-GK spectral sequences that relate the bi-Hermitian…

In this study, we consider the generalized complex number system $C_{\rm{p}} = \left\{ {x + iy\;:\;x,y \in R,\;{i^2} = {\rm{p}} \in R} \right\}$ corresponding to elliptical complex number, parabolic complex number and hyperbolic complex…

We give a complex polarized variation of Hodge structure over a compact K"ahler manifold $M$ which controls all finite-dimensional complex polarized variations of Hodge structure over $M$ and their tensor relations. As a corollary, we…

A product of K\"ahler manifolds also carries a K\"ahler metric. In this short note we would like to study the product of generalized $p-$K\"ahler manifolds, compact or not. The results we get extend the known results (balanced, SKT, sG…

We introduce a trick of dealing with $L^2$ estimates of $\bar{\partial}$ with singular weights on complete K\"ahler domains.

We discuss critical elliptic systems in potential form. We prove existence, multiplicity, and compactness of solutions.

In this paper we study dually flat spaces arising from Delzant polytopes equipped with a symplectic potential together with their corresponding toric K\"ahler manifolds as their torifications.We introduce a dually flat structure and the…

It is known that holomorphic Poisson structures are closely related to theories of generalized K\"{a}hler geometry and bi-Hermitian structures. In this article, we introduce quantization of holomorphic Poisson structures which are closely…

Analytic-bilinear approach for construction and study of integrable hierarchies is discussed. Generalized multicomponent KP and 2D Toda lattice hierarchies are considered. This approach allows to represent generalized hierarchies of…

A known general class of superintegrable systems on 2D spaces of constant curvature can be defined by potentials separating in (geodesic) polar coordinates. The radial parts of these potentials correspond either to an isotropic harmonic…

We define $(p,q)$ hermitian geometry as the target space geometry of the two dimensional $(p,q)$ supersymmetric sigma model. This includes generalised K\"{a}hler geometry for $(2,2)$, generalised hyperk\"{a}hler geometry for $(4,2)$, strong…

It is known that nilpotent orbits in a complex simple Lie algebra admit hyperK\"ahler metrics with a single function that is a global potential for each of the K\"ahler structures (a hyperK\"ahler potential). In an earlier paper the authors…

Recently, in [18] the authors gave some results on the structure, capability and the Schur multiplier of generalized Heisenberg Lie superalgebra. In this work we try to extend these concepts to the case of generalized Heisenberg Lie…

We consider the generalized Kahler structures (g,J_+,J_-) that arise on a hyperkahler manifold (M,g,I,J,K) when we choose J_+ and J_- from the twistor space of M. We find a relation between semichiral and arctic superfields which can be…

We describe a uniform way of obtaining basic hypergeometric functions as limits of the elliptic beta integral. This description gives rise to the construction of a polytope with a different basic hypergeometric function attached to each…

We consider in R^2 the generalized elastica functional defined, for smooth functions, as the p-elastica energies of the level lines integrated over all levels. Extending the functional to L1, we study its L1-lower semicontinuous envelope…

A general method to easily build global and relative operators for any number n of elementary systems if they are defined for 2 is presented. It is based on properties of the morphisms valued in the tensor products of algebras of the…

We show a very simple and general total second variation formula for Perelman's $\mathcal{W}$-functional at arbitrary points in the space of Riemannian metrics. Moreover we perform a study of the properties of the variations of K\"ahler…

In this paper we define a canonical Poisson structure on a normal generalized contact metric space and use this structure to define a generalized Sasakian structure. We show also that this canonical Poisson structure enables us to…

In this paper we present a conjecture on the construction of generalised elliptic units above number fields with exactly one complex place. These elliptic units obtained as values of multiple elliptic Gamma functions. These form a…