Einstein metrics and Yamabe invariants of weighted projective spaces
Jeff A. Viaclovsky
TL;DR
This paper investigates the existence of Einstein metrics on weighted projective spaces using an orbifold Hitchin-Thorpe inequality and provides estimates for their orbifold Yamabe invariants.
Contribution
It introduces an orbifold version of the Hitchin-Thorpe inequality to determine non-existence of Einstein metrics and offers new estimates for orbifold Yamabe invariants.
Findings
Certain weighted projective spaces do not admit orbifold Einstein metrics.
Derived estimates for the orbifold Yamabe invariants of weighted projective spaces.
Applied orbifold geometric inequalities to analyze metric properties.
Abstract
An orbifold version of the Hitchin-Thorpe inequality is used to prove that certain weighted projective spaces do not admit orbifold Einstein metrics. Also, several estimates for the orbifold Yamabe invariants of weighted projective spaces are proved.
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