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The Dirac spectrum of Bieberbach manifolds
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Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“Thus, out of the 28 classes, 1 is supersymmetric and stable, 26 have known bubbles of nothing, but there is one left (class G3 in [27]) for which no bubble of nothing was known.”
From Nothing is certain in string compactifications (2020) · cites this paper as [28]
In the citing paper
“we will also construct smooth instantons mediating the decay to nothing of the 27 non-supersymmetric compactifications M D-3 × T 3 /Γ in [27,28], including the missing case where the compact space is G3 [27].”
From Nothing is certain in string compactifications (2020) · cites this paper as [28]
In the citing paper
“These manifolds are all spin, and taking into account the spin structure, there are 28 different possibilities.”
From Nothing is certain in string compactifications (2020) · cites this paper as [28]
In the citing paper
“27 of them do not admit covariantly constant spinors; they break necessarily all supersymmetry”
From Nothing is certain in string compactifications (2020) · cites this paper as [28]
Citations
Cites
No references could be resolved yet.
Research works printed but not linked: 11
- Bär, 1996, The Dirac operator on space forms of positive curvature, J. Math. Soc. Jpn., 48, 69, 10.2969/jmsj/04810069 · DOI
- Bieberbach, 1911, Über die Bewegungsgruppe der Euklidischen Räume 1, Math. Ann., 70, 297, 10.1007/BF01564500 · DOI
- Bieberbach, 1912, Über die Bewegungsgruppe der Euklidischen Räume 2, Math. Ann., 72, 400, 10.1007/BF01456724 · DOI
- L.S. Charlap, Bieberbach Groups and Flat Manifolds, Springer, New York, 1986. · DOI
- Friedrich, 1981, Zur Existenz paralleler Spinorfelder über Riemannschen Mannigfaltigkeiten, Colloq. Math., 44, 277, 10.4064/cm-44-2-277-290 · DOI
- Friedrich, 1984, Zur Abhängigkeit des Dirac-Operators von der Spin-Struktur, Colloq. Math., 47, 57, 10.4064/cm-48-1-57-62 · DOI
- T. Friedrich, Dirac-Operatoren in der Riemannschen Geometrie, Vieweg, Braunschweig, 1997. · DOI
- Hantzsche, 1935, Dreidimensionale euklidische Raumformen, Math. Ann., 110, 593, 10.1007/BF01448045 · DOI
- T. Sakai, Riemannian Geometry, American Mathematical Society, Providence, RI, 1996. · DOI
- E.T. Whittaker, G.N. Watson, A Course in Modern Analysis, 4th Edition, Cambridge University Press, London, 1927.
- J.A. Wolf, Spaces of Constant Curvature, McGraw-Hill, New York, 1967.
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
- Pfäffle, F.
- Venue
- Journal of Geometry and Physics
- Publisher
- Elsevier BV
- Published
- 2000-10
- Volume
- 35
- Issue
- 4
- Pages
- 367-385
- ISSN
- 0393-0440
- Cited by
- 35
- References
- 0
- Language
- en
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- CoChat. (2026). Citation check: The Dirac spectrum of Bieberbach manifolds. https://app.cochat.ai/papers/10.1016/s0393-0440(00)00005-x
- The paper
- Pfäffle, F. (2000). The Dirac spectrum of Bieberbach manifolds. Journal of Geometry and Physics. https://doi.org/10.1016/s0393-0440(00)00005-x
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
