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

2020/12/27 by Brian Klatt, Klatt, Brian
Mathematics · #53C25 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C25

paper · pdf · doi:10.48550/arxiv.2012.13848

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

arxiv created 2021/06/25 · arxiv updated 2021/06/29

Abstract

We prove that a compact, connected, and oriented 4-dimensional gradient m-quasi-Einstein manifold with m∈ [1, ∞] 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 S⁴ or a connected sum of some number of S²× S² when the potential function is nontrivial.

Related

• Spin Manifolds, Einstein Metrics, and Differential Topology
• Hitchin-Thorpe Inequality for Noncompact Einstein 4-Manifolds
• 4-Manifolds without Einstein Metrics
• Monopole classes and Einstein metrics
• Geometric inequalities for quasi-Einstein manifolds