Related papers: Subanalytic Bundles and Tubular Neighbourhoods of …

In the paper we investigate submanifolds in a tangent bundle endowed with g-natural metric G, defined by a vector field on a base manifold. We give a sufficient condition for a vector field on M to defined totally geodesic submanifold in…

In accordance with the Bing-Borsuk conjecture, we show that if X is an n-dimensional homogeneous metric ANR compactum and x\in X, then there is a local basis at x consisting of connected open sets U such that the cohomological properties of…

We prove group existence and structure theorems in a general setting of tame topological theories. More precisely, we identify a linear/non-linear dividing line -- called topological 1-basedness -- among the class of t-minimal theories with…

The study of certain differential operators between Sobolev spaces of sections of vector bundles on compact manifolds equipped with rough metric is closely related to the study of locally Sobolev functions on domains in the Euclidean space.…

Let P be a parabolic subgroup of a semisimple complex Lie group G defined by a subset \Sigma of simple roots of G, and let E_\phi be a homogeneous vector bundle over the flag manifold G/P corresponding to a linear representation \phi of P.…

We study the linearization of line bundles and the local structure of actions of connected linear algebraic groups, in the setting of seminormal varieties. We show that several classical results about normal varieties extend to that…

We investigate the formal principle for holomorphic line bundles on neighborhoods of an analytic subset of a complex manifold mainly in the case where it can be realized as an open subset of a compact K\"ahler manifold. Our approach…

Approximate lattices of Euclidean spaces, also known as Meyer sets, are aperiodic subsets with fascinating properties. In general, approximate lattices are defined as approximate subgroups of locally compact groups that are discrete and…

We survey results on the distribution of zeros of random polynomials and of random holomorphic sections of line bundles, especially for large classes of probability measures on the spaces of holomorphic sections. We provide furthermore some…

In this article we prove that for a closed, not necessarily compact, submanifold $N$ of a possibly non-complete Finsler manifold $(M, F)$, the cut time map is always positive. As a consequence, we prove the existence of a tubular…

Consider a continuous bundle $\mathcal{E}\to X$ of Banach/Hilbert spaces or Banach/$C^*$-algebras over a paracompact base space, equivariant for a compact Lie group $\mathbb{U}$ operating on all structures involved. We prove that in all…

We construct examples of non-isomorphic algebraic vector bundles on the punctured affine space with isomorphic pullbacks to the smooth quadric.

Let C be an irreducible smooth projective curve, of genus at least two, defined over an algebraically closed field of characteristic zero. For a fixed line bundle L on C, let M_C(r,L) be the coarse moduli space of semistable vector bundles…

We study the distribution of the common zero sets of $m$-tuples of holomorphic sections of powers of $m$ singular Hermitian pseudo-effective line bundles on a compact K\"ahler manifold. As an application, we obtain sufficient conditions…

Let $E$ be a holomorphic vector bundle over a compact K\"{a}hler manifold $(X,\omega)$ with negative sectional curvature $sec\leq -K<0$, $\Delta_{E}$ be the Chern connection on $E$. In this article we show that if…

Suppose that $X$ is a projective manifold whose tangent bundle $T_X$ contains a locally free strictly nef subsheaf. We prove that $X$ is isomorphic to a projective bundle over a hyperbolic manifold. Moreover, if the fundamental group…

Let \(X\) be an irreducible smooth complex projective variety, and let \(G\) be a connected reductive linear algebraic group over \(\mathbb{C}\). In this paper, we first classify integrable transitive algebraic Lie algebroids on $X$. We…

We shall prove that a moduli space of flat irreducible Lie algebroid connections over a compact manifold has locally a natural structure of a smooth differentiable space. This is a generalization of some well known results for the moduli…

Let $X$ be a real Banach space with an unconditional basis (e.g., $X=\ell_2$ Hilbert space), $\Omega\subset X$ open, $M\subset\Omega$ a closed split real analytic Banach submanifold of $\Omega$, $E\to M$ a real analytic Banach vector…

Let $X$ be a complex manifold and $L$ be a holomorphic line bundle on $X$. Assume that $L$ is semi-positive, namely $L$ admits a smooth Hermitian metric with semi-positive Chern curvature. Let $Y$ be a compact K\"ahler submanifold of $X$…