The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
Manifolds of Positive Scalar Curvature: A Progress Report
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“In particular, any compact spin four-manifold with nonvanishing integrated Dirac index, S Â(R), does not admit a metric of positive scalar curvature.”
From Nothing is certain in string compactifications (2020) · cites this paper as [86]
In the citing paper
“Yet not every manifold admits a metric of everywhere positive scalar curvature.This is a problem which has been exhaustively studied by mathematicians, and a very clear survey of the question can be found in [86].”
From Nothing is certain in string compactifications (2020) · cites this paper as [86]
In the citing paper
“In dimension bigger than or equal to 5, a stronger statement, know as the trichotomy theorem [86], implies that a compact manifold which admits a Ricci-flat metric will not admit a metric of positive scalar curvature.”
From Nothing is certain in string compactifications (2020) · cites this paper as [86]
In the citing paper
“Now, on every smooth compact manifold of dimension ≥ 3, it is a fact that every metric is conformal to a different metric of constant scalar curvature (this is known as the solution to the”
From Nothing is certain in string compactifications (2020) · cites this paper as [86]
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Cites
Kervaire, M. A., & Milnor, J. W. (1963) · The Annals of Mathematics · doi:10.2307/1970128 · Cited by 904
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Cited by
Nothing is certain in string compactifications
Etxebarria, I. G., Montero, M., Sousa, K., & Valenzuela, I. (2020) · Journal of High Energy Physics · doi:10.1007/jhep12(2020)032 · Cited by 87
Metadata
- Authors
- Rosenberg, J.
- Venue
- Surveys in Differential Geometry
- Publisher
- International Press of Boston
- Published
- 2006
- Volume
- 11
- Issue
- 1
- Pages
- 259-294
- ISSN
- 1052-9233
- 2164-4713
- Cited by
- 25
- References
- 1
- Language
- en
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