Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 19 (2023), 027, 11 pages      arXiv:2302.12060      https://doi.org/10.3842/SIGMA.2023.027
Contribution to the Special Issue on Differential Geometry Inspired by Mathematical Physics in honor of Jean-Pierre Bourguignon for his 75th birthday

Yamabe Invariants, Homogeneous Spaces, and Rational Complex Surfaces

Claude LeBrun
Department of Mathematics, Stony Brook University, Stony Brook, NY 11794-3651, USA

Received February 23, 2023, in final form May 02, 2023; Published online May 07, 2023

Abstract
The Yamabe invariant is a diffeomorphism invariant of smooth compact manifolds that arises from the normalized Einstein-Hilbert functional. This article highlights the manner in which one compelling open problem regarding the Yamabe invariant appears to be closely tied to static potentials and the first eigenvalue of the Laplacian.

Key words: scalar curvature; conformal structure; Yamabe problem; diffeomorphism invariant.

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