Related papers: Quantization in geometric pluripotential theory

We establish the convexity of Mabuchi's K-energy functional along weak geodesics in the space of Kahler potentials on a compact Kahler manifold thus confirming a conjecture of Chen and give some applications in Kahler geometry, including a…

We study equations on a principal bundle over a compact complex manifold coupling connections on the bundle with K\"ahler structures in the base. These equations generalize the conditions of constant scalar curvature for a K\"ahler metric…

It's well-known in \kahler geometry that the infinite dimensional symmetric space $\hcal$ of smooth \kahler metrics in a fixed \kahler class on a polarized \kahler manifold is well approximated by finite dimensional submanifolds $\bcal_k…

The structure of nearly K\"ahler manifolds was studied by Gray in several papers. More recently, a relevant progress on the subject has been done by Nagy. Among other results, he proved that a strict and complete nearly K\"ahler manifold is…

We explain that when quantising phase spaces with varying symplectic structures, the bundle of quantum Hilbert spaces over the parameter space has a natural unitary connection. We then focus on symplectic vector spaces and their fermionic…

External potentials play a crucial role in modelling quantum systems, since, for a given inter- particle interaction, they define the system Hamiltonian. We use the metric space approach to quantum mechanics to derive, from the energy…

A Finsler metric is geodesically reversible if geodesics remain geodesics after a change of orientation. Asymmetric norms on vector spaces and Funk metrics in the interior of convex bodies are examples of geodesically reversible metrics…

We formalize the ``metric bundle'' viewpoint by defining, for any smooth $n$--manifold $M$, the open fiberwise cones $\mathcal{G}^{p,q}\subset S^2\Tstar M$ of nondegenerate symmetric bilinear forms with fixed signature $(p,q)$, and we…

We give a complete list of non-isometric bidimensional rotation invariant K\"ahler-Einstein submanifolds of a finite dimensional complex projective space endowed with the Fubini-Study metric. This solves in the aforementioned case a…

We introduce and study a novel uniformization metric model for the quasi-Fuchsian space QF(S) of a closed oriented surface S, defined through a class of C-valued bilinear forms on S, called Bers metrics, which coincide with hyperbolic…

This report introduces and investigates a family of metrics on sets of pointed Kripke models. The metrics are generalizations of the Hamming distance applicable to countably infinite binary strings and, by extension, logical theories or…

On a 3-manifold bounding a compact 4-manifold, let a conformal structure be induced from a complete Einstein metric which conformally compactifies to a K\"ahler metric. Formulas are derived for the eta invariant of this conformal structure…

In this paper we examine two basic topological properties of partial metric spaces, namely compactness and completeness. Our main result claims that in these spaces compactness is equivalent to sequential compactness. We also show that…

Various types of Lagrange and Finsler geometries and the Einstein gravity theory, and modifications, can be modelled by nonholonomic distributions on tangent bundles/ manifolds when the fundamental geometric objects are adapted to nonlinear…

Under the action of the c-map, special Kahler manifolds are mapped into a class of quaternion-Kahler spaces. We explicitly construct the corresponding Swann bundle or hyperkahler cone, and determine the hyperkahler potential in terms of the…

Let $X$ be a compact K\"ahler unibranch complex analytic space of pure dimension. Fix a big class $\alpha$ with smooth representative $\theta$ and a model potential $\phi$ with positive mass. We define and the study non-pluripolar products…

We give a new construction of strict deformation quantization of symplectic manifolds equipped with a proper Lagrangian fiber bundle structure, whose representation spaces are the quantum Hilbert spaces obtained by geometric quantization.…

In this paper we introduce and study so-called $k^*$-metrizable spaces forming a new class of generalized metric spaces, and display various applications of such spaces in topological algebra, functional analysis, and measure theory. By…

This paper develops a unified framework for observables in n-plectic geometry, extending the L_infty-algebra of Hamiltonian (n-1)-forms to Hamiltonian forms of all degrees via a degree-shifting Grassmann variable u that encodes submanifold…

Given a flat metric one may generate a local Hamiltonian structure via the fundamental result of Dubrovin and Novikov. More generally, a flat pencil of metrics will generate a local bi-Hamiltonian structure, and with additional…