Compact 4-Dimensional Spin Gradient $m$-quasi-Einstein Manifolds Satisfy the Hitchin-Thorpe Inequality when $m\ge 1$

Brian Klatt

Compact 4-Dimensional Spin Gradient $m$-quasi-Einstein Manifolds Satisfy the Hitchin-Thorpe Inequality when $m\ge 1$

Differential Geometry 2021-06-29 v3

Authors: Brian Klatt

Abstract

We prove that a compact, connected, and oriented 4-dimensional gradient $m$ -quasi-Einstein manifold with $m\in [1, \infty]$ which is additionally a spin manifold must satisfy the Hitchin-Thorpe Inequality. We show further that the homeomorphism-type of the universal cover of such a manifold is either $S^4$ or a connected sum of some number of $S^2\times S^2$ when the potential function is nontrivial.

Keywords

spin manifold gradient m-quasi-einstein hitchin-thorpe inequality 4-dimensional manifold universal cover

Cite

@article{arxiv.2012.13848,
  title  = {Compact 4-Dimensional Spin Gradient $m$-quasi-Einstein Manifolds Satisfy the Hitchin-Thorpe Inequality when $m\ge 1$},
  author = {Brian Klatt},
  journal= {arXiv preprint arXiv:2012.13848},
  year   = {2021}
}

Comments

7 pages; unintentional omission of hypothesis in main theorems corrected, minor typos fixed

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