Big vector bundles and complex manifolds with semi-positive tangent bundles

2016 ◽  
Vol 367 (1-2) ◽  
pp. 251-282 ◽  
Author(s):  
Xiaokui Yang
Keyword(s):  
Vector Bundles ◽  
Complex Manifolds ◽  
Tangent Bundles

scholarly journals On complex manifolds with positive tangent bundles

1970 ◽  
Vol 22 (4) ◽  
pp. 499-525 ◽  
Author(s):  
Shoshichi KOBAYASHI ◽  
Takushiro OCHIAI
Keyword(s):  
Complex Manifolds ◽  
Tangent Bundles

scholarly journals Holomorphic Vector Bundles on Holomorphically Convex Complex Manifolds

2006 ◽  
Vol 13 (1) ◽  
pp. 7-10
Author(s):  
Edoardo Ballico
Keyword(s):  
Vector Bundle ◽  
Complex Manifold ◽  
Vector Bundles ◽  
Open Neighborhood ◽  
Holomorphic Vector Bundle ◽  
Stein Manifold ◽  
Complex Manifolds ◽  
Holomorphic Vector Bundles

Abstract Let 𝑋 be a holomorphically convex complex manifold and Exc(𝑋) ⊆ 𝑋 the union of all positive dimensional compact analytic subsets of 𝑋. We assume that Exc(𝑋) ≠ 𝑋 and 𝑋 is not a Stein manifold. Here we prove the existence of a holomorphic vector bundle 𝐸 on 𝑋 such that is not holomorphically trivial for every open neighborhood 𝑈 of Exc(𝑋) and every integer 𝑚 ≥ 0. Furthermore, we study the existence of holomorphic vector bundles on such a neighborhood 𝑈, which are not extendable across a 2-concave point of ∂(𝑈).

scholarly journals On holomorphic maps with only fold singularities

2001 ◽  
Vol 164 ◽  
pp. 147-184
Author(s):  
Yoshifumi Ando
Keyword(s):  
Homotopy Class ◽  
Homotopy Equivalent ◽  
Line Bundles ◽  
Jet Space ◽  
Complex Manifolds ◽  
Holomorphic Maps ◽  
Regular Map ◽  
Holomorphic Map ◽  
Fold Map ◽  
Tangent Bundles

Let f : N ≡ P be a holomorphic map between n-dimensional complex manifolds which has only fold singularities. Such a map is called a holomorphic fold map. In the complex 2-jet space J2(n,n;C), let Ω10 denote the space consisting of all 2-jets of regular map germs and fold map germs. In this paper we prove that Ω10 is homotopy equivalent to SU(n + 1). By using this result we prove that if the tangent bundles TN and TP are equipped with SU(n)-structures in addition, then a holomorphic fold map f canonically determines the homotopy class of an SU(n + 1)-bundle map of TN ⊕ θN to TP⊕ θP, where θN and θP are the trivial line bundles.

scholarly journals On fuzzy subbundles of vector bundles

2003 ◽  
Vol 2003 (40) ◽  
pp. 2553-2565
Author(s):  
V. Murali ◽  
G. Lubczonok
Keyword(s):  
Vector Bundle ◽  
Tensor Product ◽  
Vector Bundles ◽  
Tangent Bundles

This paper considers fuzzy subbundles of a vector bundle. We define the operations sum, product, tensor product,Hom, and intersection of fuzzy subbundles and in each case, we characterize the corresponding flag of vector subbundles. We then propose two alternative definitions of integrability on fuzzy subbundles of a given type and discuss their naturality, merits, and shortcomings. We do these here with a view to introduce and study integrable fuzzy subbundles of tangent bundles on manifolds and foliations in further papers.

scholarly journals On the completeness of total spaces of horizontally conformal submersions

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Mohamed Tahar Kadaoui Abbassi ◽  
Ibrahim Lakrini
Keyword(s):  
Vector Bundle ◽  
General Result ◽  
Vector Bundles ◽  
Riemannian Metrics ◽  
Riemannian Submersion ◽  
Spherically Symmetric ◽  
Symmetric Metrics ◽  
Metric Topology ◽  
Unit Tangent Sphere Bundles ◽  
Tangent Bundles

Abstract In this paper, we address the completeness problem of certain classes of Riemannian metrics on vector bundles. We first establish a general result on the completeness of the total space of a vector bundle when the projection is a horizontally conformal submersion with a bound condition on the dilation function, and in particular when it is a Riemannian submersion. This allows us to give completeness results for spherically symmetric metrics on vector bundle manifolds and eventually for the class of Cheeger-Gromoll and generalized Cheeger-Gromoll metrics on vector bundle manifolds. Moreover, we study the completeness of a subclass of g-natural metrics on tangent bundles and we extend the results to the case of unit tangent sphere bundles. Our proofs are mainly based on techniques of metric topology and on the Hopf-Rinow theorem.

Sign in / Sign up

Export Citation Format

Share Document