Chern forms of holomorphic Finsler vector bundles and some applications

Horizontal Forms of Chern Type on Complex Finsler Bundles

The aim of this paper is to construct horizontal Chern forms of a holomorphic vector bundle using complex Finsler structures. Also, some properties of these forms are studied.

Finsler Geometry of Holomorphic Jet Bundles

Introduction 107 1. Holomorphic Jet Bundles 113 2. Chern Classes and Cohomology Groups: The Case of Curves 120 3. Computation of Chern Classes: The Case of Surfaces 139 4. Finsler Geometry of Projectivized Vector Bundles 148 5. Weighted Projective Spaces and Projectivized Jet Bundles 153 6. The Lemma of Logarithmic Derivatives and the Schwarz Lemma 164 7. Surfaces of General Type 173 Acknowledg...

Higgs Bundles and Holomorphic Forms

For a complex manifold X which has a holomorphic form ̟ of odd degree k, we endow E = ⊕ p≥a Λ (p,0)(X) with a Higgs bundle structure θ given by θ(Z)(φ) := {i(Z)̟} ∧ φ. The properties such as curvature and stability of these and other Higgs bundles are examined. We prove (Theorem 2, section 2, for k > 1) E and additional classes of Higgs subbundles of E do not admit Higgs-Hermitian-Yang-Mills metr...

Finsler Geometry of Projectivized Vector Bundles

Chern classes of automorphic vector bundles

1.1. Suppose X is a compact n-dimensional complex manifold. Each partition I = {i1, i2, . . . , ir} of n corresponds to a Chern number c (X) = ǫ(c1(X)∪c2(X)∪. . .∪cr(X)∩[X]) ∈ Z where c(X) ∈ H(X;Z) are the Chern classes of the tangent bundle, [X] ∈ H2n(X;Z) is the fundamental class, and ǫ : H0(X;Z) → Z is the augmentation. Many invariants of X (such as its complex cobordism class) may be expres...