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Torsionless three-dimensional Heterotic solitons with harmonic curvature are rigid

Andrei Moroianu, Miguel Pino Carmona, C. S. Shahbazi

Abstract

We prove the following rigidity result: every compact three-dimensional Heterotic soliton with vanishing torsion and harmonic curvature is rigid, namely, it is an isolated point in the moduli space.

Torsionless three-dimensional Heterotic solitons with harmonic curvature are rigid

Abstract

We prove the following rigidity result: every compact three-dimensional Heterotic soliton with vanishing torsion and harmonic curvature is rigid, namely, it is an isolated point in the moduli space.
Paper Structure (7 sections, 12 theorems, 81 equations)

This paper contains 7 sections, 12 theorems, 81 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Linearization of certain curvature operators
  4. Rigidity of hyperbolic Heterotic solitons
  5. Existence of a slice
  6. Essential deformations
  7. Heterotic solitons with harmonic curvature

Key Result

Theorem 1.1

Let $(g,\phi)$ be a torsionless, non-flat, three‑dimensional compact Heterotic soliton with vanishing torsion and harmonic curvature. Then, the vector space of essential deformations of $(g,\phi)$ is zero-dimensional.

Theorems & Definitions (24)

  • Theorem 1.1
  • Proposition 2.1
  • proof
  • Corollary 2.2
  • proof
  • Remark 2.3
  • Proposition 2.4
  • proof
  • Lemma 3.1
  • proof
  • ...and 14 more