Skip to Main Content

Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Nonconnected moduli spaces of positive sectional curvature metrics
HTML articles powered by AMS MathViewer

by Matthias Kreck and Stephan Stolz PDF
J. Amer. Math. Soc. 6 (1993), 825-850 Request permission

Abstract:

For a closed manifold $M$ let $\Re _{{\text {sec}}}^ + (M)$ (resp. $\Re _{{\text {Ric}}}^ + (M)$) be the space of Riemannian metrics on $M$ with positive sectional (resp. Ricci) curvature and let ${\text {Diff}}(M)$ be the diffeomorphism group of $M$, which acts on these spaces. We construct examples of $7$-dimensional manifolds for which the moduli space $\Re _{{\text {sec}}}^ + (M)/{\text {Diff}}(M)$ is not connected and others for which $\Re _{{\text {Ric}}}^ + (M)/{\text {Diff}}(M)$ has infinitely many connected components. The examples are obtained by analyzing a family of positive sectional curvature metrics on homogeneous spaces constructed by Aloff and Wallach, on which $SU(3)$ acts transitively, respectively a family of positive Einstein metrics constructed by Wang and Ziller on homogeneous spaces, on which $SU(3) \times SU(2) \times U(1)$ acts transitively.
References
Similar Articles
Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 6 (1993), 825-850
  • MSC: Primary 53C20; Secondary 53C21, 57R20, 58D27, 58G10
  • DOI: https://doi.org/10.1090/S0894-0347-1993-1205446-4
  • MathSciNet review: 1205446