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Compact Einstein-type manifolds with parallel Ricci tensor

Maria Andrade, Halyson Baltazar, Christopher Queiroz

Abstract

In this paper, we deduce a Bochner-type identity for compact gradient Einstein-type manifolds with boundary. As consequence, we are able to show a rigidity result for Einstein-type manifolds assuming the parallel Ricci curvature condition. Moreover, we provide a condition on the norm of the gradient of the potential function in order to classify such structures.

Compact Einstein-type manifolds with parallel Ricci tensor

Abstract

In this paper, we deduce a Bochner-type identity for compact gradient Einstein-type manifolds with boundary. As consequence, we are able to show a rigidity result for Einstein-type manifolds assuming the parallel Ricci curvature condition. Moreover, we provide a condition on the norm of the gradient of the potential function in order to classify such structures.
Paper Structure (8 sections, 58 equations)

This paper contains 8 sections, 58 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. A Bochner formula for Einstein-type manifolds
  4. Proof of Theorem \ref{['THM1Ricciparallel']}
  5. Proof of Theorem \ref{['THM1Ricciparallel']}
  6. Proof of Theorem \ref{['Thm2']}
  7. Proof of Theorem \ref{['Thm2']}
  8. Conclusion of the proof of Corollary \ref{['Co2']}

Theorems & Definitions (7)

  • proof
  • proof
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  • proof