Related papers: On Vector Bundles of Finite Order

We introduce a notion of Gieseker stability for a filtered holomorphic vector bundle $F$ over a projective manifold. We relate it to an analytic condition in terms of hermitian metrics on $F$ coming from a construction of the Geometric…

By using a certain second order differential equation, the notion of adapted coordinates on Finsler manifolds is defined and some classifications of complete Finsler manifolds are found. Some examples of Finsler metrics, with positive…

This paper investigates the curvature properties of higher direct images $ R^qf_*\Omega_{X/S}^p(E)$, where $f: X\rightarrow S$ is a family of compact K\"ahler manifolds equipped with a hermitian vector bundle $E \rightarrow X$. We derive a…

Let $P(E)$ be the projectivization of a holomorphic vector bundle $E$ over a compact complex curve $C$. We characterize the existence of an extremal K\"ahler metric on the ruled manifold $P(E)$ in terms of relative K-polystability and the…

If a sequence of Riemannian manifolds, $X_i$, converges in the pointed Gromov-Hausdorff sense to a limit space, $X_\infty$, and if $E_i$ are vector bundles over $X_i$ endowed with metrics of Sasaki-type with a uniform upper bound on rank,…

In this paper, first we prove the existence of invariant vector field on a homogeneous Finsler space with infinite series $(\alpha, \beta)$-metric and exponential metric. Next, we deduce an explicit formula for the the $S$-curvature of…

We survey the distributional properties of progressively dilating sets under projection by covering maps, focusing on manifolds of constant sectional curvature. In the Euclidean case, we review previously known results and formulate some…

Consider a very ample line bundle $ E \to X$ over a compact complex manifold, endowed with a hermitian metric of curvature $-i \omega $, and the space $\mathcal{O}(E)$ of its holomorphic sections. The Fubini--Study map associates with…

According to Horrocks (1966), a vector bundle E on the projective n-space extends stably to the projective N-space, N>n, if there exists a vector bundle on the larger space whose restriction to the smaller one is isomorphic to E plus a…

In our previous papers [Far East Journal of Mathematical Sciences, 35 (2009), 211-223] and [International Journal of Pure and Applied Mathematics, 60 (2010), 15-24] we have developed the theory of Weil prolongation, Weil exponentiability…

We consider a notion of balanced metrics for triples (X,L,E) which depend on a parameter \alpha, where X is smooth complex manifold with an ample line bundle L and E is a holomorphic vector bundle over X. For generic choice of \alpha, we…

Let $X$ be a smooth complete curve, and let $Bun_n$ be the moduli stack of rank $n$ vector bundles on $X$. Let $E$ be a local system on $X$. In a recent paper of E.Frenkel, K.Vilonen and the author, it was shown that the vanishing of a…

We study the cohomological classification of vector bundles on smooth real affine surfaces and threefolds. We show that, as was observed in joint work in A. Asok and J. Fasel and in a coming joint paper with S. Banerjee and J. Fasel, under…

We investigate when the filtration induced by Beilinson's spectral sequence splits non-canonically into a direct sum decomposition. We conclude that for any vector bundle $\mathcal{E}$ on a projective space over an algebraically closed…

We adapt the notions of stability of holomorphic vector bundles in the sense of Mumford-Takemoto and Hermitian-Einstein metrics in holomorphic vector bundles for canonically polarized framed manifolds, i.e. compact complex manifolds X…

We propose a matrix regularization of vector bundles over a general closed K\"ahler manifold. This matrix regularization is given as a natural generalization of the Berezin-Toeplitz quantization and gives a map from sections of a vector…

We consider the oriented graph whose vertices are isomorphism classes of finitely generated groups, with an edge from G to H if, for some generating set T in H and some sequence of generating sets S_i in G, the marked balls of radius i in…

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…

This paper is concerned with the holonomy of a class of spaces which includes Landsberg spaces of Finsler geometry. The methods used are those of Lie groupoids and algebroids as developed by Mackenzie. We prove a version of the…

A geodesic circle in Finsler geometry is a natural extension of that in a Euclidean space. In this paper, we apply Lie derivatives and the Cartan $Y$-connection to study geodesic circles and (infinitesimal) concircular transformations on a…