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Einstein metrics and Yamabe invariants of weighted projective spaces

Jeff A. Viaclovsky
- 30 Jun 2013 - 
- Vol. 65, Iss: 2, pp 297-311
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TLDR
In this paper, the Hitchin-Thorpe inequality is used to prove that certain weighted projective spaces do not admit orbifold Einstein metrics, and several estimates for the Yamabe invariants are proved.
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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Spectral asymmetry and Riemannian geometry. III

TL;DR: In this article, the authors present a generalization of Hirzebruch's signature theorem for the case of manifolds with boundary, which can be viewed as analogous to the Gauss-Bonnet theorem for manifold with boundary.
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Conformal deformation of a Riemannian metric to constant scalar curvature

TL;DR: In this paper, a new global idea was introduced to solve the Yamabe problem in dimensions 3, 4, and 5, and the existence of a positive solution u on M of the equation was proved in all remaining cases.
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Spectral Asymmetry and Riemannian Geometry

TL;DR: In this article, a refinement of this invariant when A is no longer positive was introduced and its geometrical significance for an important class of operators arising from Riemannian geometry was studied.
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Self-dual solutions to euclidean gravity

TL;DR: In this article, a review of Euclidean self-dual metric solutions to the Einstein equations is presented, and the authors show that these solutions have vanishing classical action and nontrivial topological invariants, and may play a role in quantum gravity resembling that of the Yang-Mills instantons.
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