Related papers: Six dimensional homogeneous spaces with holomorphi…

We consider the problem of identifying a unitary Yang-Mills connection $\nabla$ on a Hermitian vector bundle from the Dirichlet-to-Neumann (DN) map of the connection Laplacian $\nabla^*\nabla$ over compact Riemannian manifolds with…

An algebraic framework for noncommutative bundles with (quantum) homogeneous fibres is proposed. The framework relies on the use of principal coalgebra extensions which play the role of principal bundles in noncommutative geometry which…

We study the heterotic G$_2$-system on 7-dimensional 2-step nilmanifolds $M=\Gamma\backslash N$ endowed with principal torus bundles. We first prove that every invariant G$_2$-structure solving the system must be coclosed (under an…

Let (M,I,J,K) be a compact hypercomplex manifold admitting an HKT-metric. Assume that the canonical bundle of (M,I) is trivial as a holomorphic line bundle. We show that the holonomy of Obata connection on M is contained in SL(n,H). In…

Let $\Omega$ be a complex manifold, and let $X\subset \Omega$ be an open submanifold whose closure $\bar X$ is a (not necessarily compact) submanifold with smooth boundary. Let $G$ be a complex Lie group, $\Pi$ be a differentiable principal…

We disclose the mathematical structure underlying the gauge field sector of the recently constructed non-abelian superconformal models in six spacetime dimensions. This is a coupled system of 1-form, 2-form, and 3-form gauge fields. We show…

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 study Hermitian metrics with a Gauduchon connection being "K\"ahler-like", namely, satisfying the same symmetries for curvature as the Levi-Civita and Chern connections. In particular, we investigate $6$-dimensional solvmanifolds with…

We use the natural lifts of the fundamental tensor field g to the cotangent bundle T*M of a Riemannian manifold (M,g), in order to construct an almost Hermitian structure (G,J) of diagonal type on T*M. The obtained almost complex structure…

This series of papers is devoted to an open-ended project aimed at the solution of Hilbert's sixth problem (concerning joint axiomatization of physics and probability theory) proposed to be constructed in the framework of an all-embracing…

It was proven by Hitchin that any solution of his evolution equations for a half-flat SU(3)-structure on a compact six-manifold M defines an extension of M to a seven-manifold with holonomy in G_2. We give a new proof, which does not…

Let $X$ be a compact complex manifold of dimension $n$ and let $m$ be a positive integer with $m\leq n$. Assume that $X$ admits a K\"ahler metric $\omega$ and a weakly positive, $\partial\bar\partial$-closed, smooth $(n-m,\,n-m)$-form…

A class of $ G $-invariant Einstein-Yang-Mills (EYM) systems with cosmological constant on homogeneous spaces $ G / H $, where $ G $ is a semisimple compact Lie group, is presented. These EYM--systems can be obtained in terms of dimensional…

This article is based on the methods developed in [AGG]. We construct a complex hyperbolic structure on a trivial disc bundle over a closed orientable surface $\Sigma$ (of genus 2) thus solving a long standing problem in complex hyperbolic…

We give a necessary and sufficient condition for a 2-dimensional Riemannian manifold to be locally isometrically immersed into a 3-dimensional homogeneous manifold with a 4-dimensional isometry group. The condition is expressed in terms of…

Let $M(n,\xi)$ be the moduli space of stable vector bundles of rank $n\geq 3$ and fixed determinant $\xi$ over a smooth projective algebraic curve $X$ over $\mathbb{C}$ of genus $g\geq 4.$ We use the gonality of the curve and $r$-Hecke…

We consider a dimensional reduction of the (deformed) Hermitian Yang-Mills condition on $S^1$-invariant K\"ahler Einstein $6$-manifolds. This allows us to reformulate the (deformed) Hermitian Yang-Mills equations in terms of data on the…

We consider strict and complete nearly Kaehler manifolds with the canonical Hermitian connection. The holonomy representation of the canonical Hermitian connection is studied. We show that a strict and complete nearly Kaehler is locally a…

A new framework for noncommutative complex geometry on quantum homogeneous spaces is introduced. The main ingredients used are covariant differential calculi and Takeuchi's categorical equivalence for faithfully flat quantum homogeneous…

Let $(G,H,\sigma)$ be a symmetric pair and $\mathfrak{g}=\mathfrak{m}\oplus\mathfrak{h}$ the canonical decomposition of the Lie algebra $\mathfrak{g}$ of $G$. We denote by ${\nabla}^0$ the canonical affine connection on the symmetric space…