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Robinson manifolds and the Chern-Robinson connection

Robert Petit

Abstract

In this article, we define the Chern-Robinson connection on the complexify tangent bundle of an almost Robinson manifold and we study the curvature associated to. Various Bianchi identities are obtained together with an application to geometry of some Robinson manifolds.

Robinson manifolds and the Chern-Robinson connection

Abstract

In this article, we define the Chern-Robinson connection on the complexify tangent bundle of an almost Robinson manifold and we study the curvature associated to. Various Bianchi identities are obtained together with an application to geometry of some Robinson manifolds.
Paper Structure (7 sections, 22 theorems, 251 equations)

This paper contains 7 sections, 22 theorems, 251 equations.

Table of Contents

  1. Introduction
  2. Optical and Robinson manifolds
  3. Fefferman-Robinson manifold
  4. Connection and curvature
  5. Optical conformal invariant tensor on almost Fefferman-Robinson manifolds
  6. Second Bianchi identity and applications
  7. Appendix

Key Result

Proposition 2.1

Let $(M^{2m+2},g,\mathcal{N},\mathcal{R},\mathcal{R}^{*})$ be an almost Fefferman-Robinson manifold together with $(\nu_{}^{},\nu_{}^{*})$ adapted $g$-optical pairing. Then

Theorems & Definitions (47)

  • Definition 2.1
  • Definition 2.2
  • Example 2.1
  • Remark 2.1
  • Definition 2.3
  • Remark 2.2
  • Definition 2.4
  • Definition 2.5
  • Definition 2.6
  • Example 2.2
  • ...and 37 more