The structure of compact Ricci-flat Riemannian manifolds
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If b1>0, the Ricci-flat space M_int of dimension D-4 can be written as a free quotient of T^k × M~^{D-4-k}_int where M~ is also Ricci-flat.
“In the case where b 1 > 0, the Ricci-flat space M int of dimension D -4 can be written as a free quotient of T k × ˜ M D -4 -k int where ˜ M D -4 -k int is also Ricci-flat [57].”
From Gravitational memory and compact extra dimensions (2022) · cites this paper as [57]
Theorem 4.1 (§4) gives a free finite quotient of a flat k-torus times a Ricci-flat (n−k)-manifold, with k equal to the first Betti number. It applies to compact connected Ricci-flat manifolds; the citing sentence does not state that restriction, so the source does not support the claim for Ricci-flat spaces generally. (LLM, conf=0.85)
Experimental — accuracy not yet measuredM_int is a free quotient of a Riemannian product of a torus and a connected Ricci-flat space with vanishing b1.
“However the decomposition theorem of [57] states that M int is a free quotient of a Riemannian product of a torus and a connected Ricci-flat space with vanishing b 1 .”
From Gravitational memory and compact extra dimensions (2022) · cites this paper as [57]
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Research works printed but not linked: 8
- E. Calabi, On Kdhler manifolds with vanishing canonical class, Algebraic Geometry and Topology, A symposium in honor of S. Lefschetz, Princeton University Press, Princeton, 1957, 78-89.
- Linearization stability of nonlinear partial differential equations, Proc. Sympos. Pure Math., Vol. 27, Amer. Math. Soc, 1974, 748-792.
- Courbure, nombres de Betti, et espaces symetriques, Proc. Internat. Congress Math. (Cambridge, 1950), Amer. Math. Soc, Vol. II, 1952, 216-223.
- E. Nelson, Tensor analysis, Math. Notes, Princeton University Press, Princeton, 1967.
- E. Spanier, The homology of Kummer manifolds, Proc. Amer. Math. Soc. 7 (1956) 155-160.
- T. J. Willmore, On compact riemannian manifolds with zero Ricci curvature, Proc. Edinburgh Math. Soc. 10 (1956) 131-133.
- Spaces of constant curvature, 2nd edition, J. A. Wolf, Berkeley, 1972.
- K. Yano & S. Bochner, Curvature and Betti numbers, Annals of Math. Studies, No. 32, Princeton University Press, Princeton, 1953.
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Gravitational memory and compact extra dimensions
Ferko, C., Satishchandran, G., & Sethi, S. (2022) · Physical Review D · doi:10.1103/physrevd.105.024072 · Cited by 20 · see citing works
- Authors
- Fischer, A. E., & Wolf, J. A.
- Venue
- Journal of Differential Geometry
- Publisher
- International Press of Boston
- Published
- 1975-01-01
- Volume
- 10
- Issue
- 2
- Pages
- 277-288
- ISSN
- 0022-040X (ISSN-L)
- OpenAlex
- W1606583418
- Cited by
- 39
- References
- 0
- Citations by year
- 2026: 1 · 2025: 1 · 2023: 2 · 2022: 3 · 2021: 3 · 2020: 3 · 2019: 2 · 2018: 2 · 2017: 2 · 2016: 1 · 2015: 4 · 2013: 1
- FWCI
- 0.50
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Journal of Differential Geometry (publishedVersion)
- Project Euclid (Cornell University) (submittedVersion)
- Funders
- National Science Foundation
- Adolph C. and Mary Sprague Miller Institute for Basic Research in Science, University of California Berkeley
- Topics
- Physical Sciences › Mathematics › Geometry and Topology › Geometry and complex manifolds
- Physical Sciences › Mathematics › Applied Mathematics › Geometric Analysis and Curvature Flows
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Advanced Differential Geometry Research
- Keywords
- Ricci-flat manifolds, compact Riemannian manifolds, Ricci curvature
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