Vanishing theorems for tensor powers of a positive vector bundle

1988 ◽  
pp. 86-105 ◽  
Author(s):  
Jean-Pierre Demailly
Keyword(s):  
Vector Bundle ◽  
Vanishing Theorems ◽  
Positive Vector ◽  
Positive Vector Bundle ◽  
Tensor Powers

Vanishing theorems for tensor powers of an ample vector bundle

1988 ◽  
Vol 91 (1) ◽  
pp. 203-220 ◽  
Author(s):  
Jean-Pierre Demailly
Keyword(s):  
Vector Bundle ◽  
Vanishing Theorems ◽  
Ample Vector Bundle ◽  
Tensor Powers

scholarly journals On Vanishing Theorems for Vector Bundle Valued p-Forms and their Applications

2011 ◽  
Vol 304 (2) ◽  
pp. 329-368 ◽  
Author(s):  
Yuxin Dong ◽  
Shihshu Walter Wei
Keyword(s):  
Vector Bundle ◽  
Vanishing Theorems

scholarly journals The Weitzenböck Type Curvature Operator for Singular Distributions

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 365
Author(s):  
Paul Popescu ◽  
Vladimir Rovenski ◽  
Sergey Stepanov
Keyword(s):  
Riemannian Manifold ◽  
Vector Bundle ◽  
Tangent Bundle ◽  
Null Space ◽  
Curvature Operator ◽  
Vanishing Theorems ◽  
Lie Algebroid ◽  
Decomposition Formula ◽  
Adjoint Operators ◽  
Type Decomposition

We study geometry of a Riemannian manifold endowed with a singular (or regular) distribution, determined as an image of the tangent bundle under smooth endomorphisms. Following construction of an almost Lie algebroid on a vector bundle, we define the modified covariant and exterior derivatives and their L 2 adjoint operators on tensors. Then, we introduce the Weitzenböck type curvature operator on tensors, prove the Weitzenböck type decomposition formula, and derive the Bochner–Weitzenböck type formula. These allow us to obtain vanishing theorems about the null space of the Hodge type Laplacian. The assumptions used in the results are reasonable, as illustrated by examples with f-manifolds, including almost Hermitian and almost contact ones.

scholarly journals (k, s)-POSITIVITY AND VANISHING THEOREMS FOR COMPACT KÄHLER MANIFOLDS

2011 ◽  
Vol 22 (04) ◽  
pp. 545-576 ◽  
Author(s):  
QILIN YANG
Keyword(s):  
Line Bundle ◽  
Vector Bundles ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Vanishing Theorems ◽  
Positive Vector ◽  
Holomorphic Vector Bundles ◽  
Positive Line Bundle ◽  
Algebraic Manifolds ◽  
Positive Line

We study the (k, s)-positivity for holomorphic vector bundles on compact complex manifolds. (0, s)-positivity is exactly the Demailly s-positivity and a (k, 1)-positive line bundle is just a k-positive line bundle in the sense of Sommese. In this way we get a unified theory for all kinds of positivities used for semipositive vector bundles. Several new vanishing theorems for (k, s)-positive vector bundles are proved and the vanishing theorems for k-ample vector bundles on projective algebraic manifolds are generalized to k-positive vector bundles on compact Kähler manifolds.

VANISHING THEOREMS ON STRONGLY Q-CONVEX MANIFOLDS

2005 ◽  
Vol 02 (03) ◽  
pp. 467-483 ◽  
Author(s):  
O. ABDELKADER ◽  
S. SABER
Keyword(s):  
Vector Bundle ◽  
Convex Domain ◽  
Holomorphic Vector Bundle ◽  
Kähler Manifold ◽  
Vanishing Theorems ◽  
Cohomology Groups ◽  
Kahler Manifold

Let X be strongly q-convex domain of an n-dimensional Kähler manifold M and E be a holomorphic vector bundle over M. Then, if E satisfies certain positivity conditions, we prove vanishing theorems for the [Formula: see text]-cohomology groups of X with values in E.

scholarly journals Generalized vanishing theorems for Yukawa couplings in heterotic compactifications

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Lara B. Anderson ◽  
James Gray ◽  
Magdalena Larfors ◽  
Matthew Magill ◽  
Robin Schneider
Keyword(s):  
Vector Bundles ◽  
Geometric Approach ◽  
Low Energy ◽  
Geometric Features ◽  
Vanishing Theorems ◽  
Vanishing Theorem ◽  
Alternative Derivation ◽  
Yukawa Couplings ◽  
Geometric Methods ◽  
Higher Dimensional

Abstract Heterotic compactifications on Calabi-Yau threefolds frequently exhibit textures of vanishing Yukawa couplings in their low energy description. The vanishing of these couplings is often not enforced by any obvious symmetry and appears to be topological in nature. Recent results used differential geometric methods to explain the origin of some of this structure [1, 2]. A vanishing theorem was given which showed that the effect could be attributed, in part, to the embedding of the Calabi-Yau manifolds of interest inside higher dimensional ambient spaces, if the gauge bundles involved descended from vector bundles on those larger manifolds. In this paper, we utilize an algebro-geometric approach to provide an alternative derivation of some of these results, and are thus able to generalize them to a much wider arena than has been considered before. For example, we consider cases where the vector bundles of interest do not descend from bundles on the ambient space. In such a manner we are able to highlight the ubiquity with which textures of vanishing Yukawa couplings can be expected to arise in heterotic compactifications, with multiple different constraints arising from a plethora of different geometric features associated to the gauge bundle.

Euler classes of vector bundles over manifolds

2021 ◽  
Vol 71 (1) ◽  
pp. 199-210
Author(s):  
Aniruddha C. Naolekar
Keyword(s):  
Vector Bundle ◽  
Vector Bundles ◽  
Euler Class ◽  
Homology Sphere ◽  
Rational Homology ◽  
Rational Homology Sphere ◽  
Orientable Manifolds

Abstract Let 𝓔 k denote the set of diffeomorphism classes of closed connected smooth k-manifolds X with the property that for any oriented vector bundle α over X, the Euler class e(α) = 0. We show that if X ∈ 𝓔2n+1 is orientable, then X is a rational homology sphere and π 1(X) is perfect. We also show that 𝓔8 = ∅ and derive additional cohomlogical restrictions on orientable manifolds in 𝓔 k .

scholarly journals WEAKLY UNIFORM RANK TWO VECTOR BUNDLES ON MULTIPROJECTIVE SPACES

2011 ◽  
Vol 84 (2) ◽  
pp. 255-260
Author(s):  
EDOARDO BALLICO ◽  
FRANCESCO MALASPINA
Keyword(s):  
Vector Bundle ◽  
Vector Bundles ◽  
Splitting Type ◽  
Multiprojective Spaces

AbstractHere we classify the weakly uniform rank two vector bundles on multiprojective spaces. Moreover, we show that every rank r>2 weakly uniform vector bundle with splitting type a1,1=⋯=ar,s=0 is trivial and every rank r>2 uniform vector bundle with splitting type a1>⋯>ar splits.

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