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Special Hermitian metrics

Cristian Ciulică

Abstract

We study the stability at blow-up and deformations of a class of Hermitian metrics whose fundamental two-form $ω$ satisfies the condition $\partial \bar \partial ω^k=0$, for any $k$ between 1 and $n-1$ (where $n$ is the complex dimension of the manifold). We are motivated by the existence of compact complex manifold supporting such metrics.

Special Hermitian metrics

Abstract

We study the stability at blow-up and deformations of a class of Hermitian metrics whose fundamental two-form satisfies the condition , for any between 1 and (where is the complex dimension of the manifold). We are motivated by the existence of compact complex manifold supporting such metrics.

Paper Structure

This paper contains 8 sections, 11 theorems, 71 equations.

Table of Contents

  1. Introduction
  2. Conventions and notations
  3. Deformations of special Hermitian metrics
  4. Review of deformation theory
  5. Stability of special Hermitian metrics at deformations
  6. Blow-up of special Hermitian metrics
  7. Basic facts about blow-up
  8. Stability of special Hermitian metrics at blow-up

Key Result

proposition Proposition 3.1

(lry) Let $\phi \in A^{0,1}(T^{1,0}M)$. We have: i.e.:

Theorems & Definitions (30)

  • definition Definition 2.1
  • definition Definition 3.2
  • definition Definition 3.3
  • definition Definition 3.4
  • remark Remark 3.1
  • definition Definition 3.5
  • proposition Proposition 3.1
  • remark Remark 3.2
  • proof
  • remark Remark 3.3
  • ...and 20 more