Related papers: Hermitian geometry on resolvent set(I)

In this paper, we prove a conjecture raised by Angella, Otal, Ugarte, and Villacampa recently, which states that if the Strominger connection (also known as Bismut connection) of a compact Hermitian manifold is K\"ahler-like, in the sense…

In this article we study the field of Hilbertian metrics and positive definit (pd) kernels on probability measures, they have a real interest in kernel methods. Firstly we will make a study based on the Alpha-Beta-divergence to have a…

A canonical hyperkaehler metric on the total space $T^*M$ of a cotangent bundle to a complex manifold $M$ has been constructed recently by the author (see alg-geom/9710026). This paper presents the results of alg-geom/9710026 in a…

For a bounded domain $D \subset \mathbb{C}^n$, let $K_D = K_D(z) > 0$ denote the Bergman kernel on the diagonal and consider the reproducing kernel Hilbert space of holomorphic functions on $D$ that are square integrable with respect to the…

Let L be a holomorphic line bundle with a positively curved singular Hermitian metric over a complex manifold X. One can define naturally the sequence of Fubini-Study currents associated to the space of square integrable holomorphic…

In a recent work, Kai Tang conjectured that any compact Hermitian manifold with non-zero constant mixed curvature must be K\"ahler. He confirmed the conjecture in complex dimension $2$ and for Chern K\"ahler-like manifolds in general…

We present a uniform framework generalising and extending the classical theories of projective differential geometry, c-projective geometry, and almost quaternionic geometry. Such geometries, which we call \emph{projective parabolic…

We study complex non-K\"ahler manifolds with Hermitian metrics being locally conformal to metrics with special cohomological properties. In particular, we provide examples where the existence of locally conformal holomorphic-tamed…

A well known notion of $k$-rectifiable set can be formulated in any metric space using Lipschitz images of subsets of $\mathbb{R}^k$. We prove some characterizations of $k$-rectifiability, when the metric space is an arbitrary homogeneous…

We develop Berezin-Toeplitz quantization in a non-compact complex geometric setting. Let $(X,\Theta)$ be a Hermitian manifold, $(L,h^L)$ a positive holomorphic line bundle, and $(E,h^E)$ a holomorphic Hermitian vector bundle. Assuming that…

We give a dynamical description, in terms of a Weil-type zeta function, to the holomorphic torsion with coefficients for certain compact Hermitian locally symmetric manifolds, whose connected group G of isometries of the universal cover has…

We study the space of complete Riemannian metrics of nonnegative curvature on the plane equipped with the C^k topology. If k is infinite, we show that the space is homeomorphic to the separable Hilbert space. For any k we prove that the…

A discrete $N-$point Runge-Kutta version $H^{(N)}({\lambda})$ of one of the simplest non-Hermitian square-well Hamiltonians with real spectrum is studied. A complete set of its possible hermitizations (i.e., of the eligible metrics…

An elementary set of non-Hermitian $N$ by $N$ matrices $H^{(N)}(\lambda) \neq [ H^{(N)}(\lambda)]^\dagger$ with real spectra is considered, assuming that each of these matrices represents a selfadjoint quantum Hamiltonian in an {\it ad hoc}…

We study the sheaf of locally square integrable holomorphic section of vector bundle with semi-positive curved singular Hermitian metric. We confirm the coherence when its induced determinant metric has analytic singularities.

The Lipschitz geometry of segments of the infinite Hamming cube is studied. Tight estimates on the distortion necessary to embed the segments into spaces of continuous functions on countable compact metric spaces are given. As an…

Let $(G,d)$ be a metric space with the counting measure $\mu$ satisfying some growth conditions. Let $\omega(x,y)=(1+d(x,y))^\delta$ for some $0<\delta\leq1$. Let $0<p\leq1$. Let $\mathcal A_{p\omega}$ be the collection of kernels $K$ on…

We use techniques from both real and complex algebraic geometry to study K-theoretic and related invariants of the algebra C(X) of continuous complex-valued functions on a compact Hausdorff topological space X. For example, we prove a…

The classical Hurwitz spaces, that parameterize compact Riemann surfaces equipped with covering maps to ${\mathbb P}_1$ of fixed numerical type with simple branch points, are extensively studied in the literature. We apply deformation…

We derive a canonical symmetry reduction associated to a compact non-K\"ahler Bismut-Hermitian-Einstein manifold. In real dimension $6$, the transverse geometry is conformally K\"ahler, and we give a complete description in terms of a…