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On the Hitchin-Thorpe inequality for gradient Ricci 4-solitons

Amir Babak Aazami

Abstract

We show that if an oriented closed 4-manifold $M$ admits a Ricci soliton metric, then its Euler characteristic and signature must satisfy $$χ(M) \geq \frac{3}{2}|τ(M)| - \frac{1}{16π^2}\!\int_M |\mathring{\text{Ric}}|^2,$$ where $\mathring{\text{Ric}}$ is the traceless Ricci tensor of the metric.

On the Hitchin-Thorpe inequality for gradient Ricci 4-solitons

Abstract

We show that if an oriented closed 4-manifold admits a Ricci soliton metric, then its Euler characteristic and signature must satisfy where is the traceless Ricci tensor of the metric.

Paper Structure

This paper contains 3 sections, 18 equations.

Table of Contents

  1. Introduction
  2. Proof of eqn:HT_sol
  3. References

Theorems & Definitions (1)

  • proof