Einstein metrics and complex structures
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Kovalev has sketched a general deformation theory for asymptotically cylindrical Calabi-Yau manifolds, but his parameter count is not entirely accurate and he needs to assume an appropriate analog of the Tian-Todorov theorem, which seems still unknown.
“Indeed, Kovalev [35] has sketched a general deformation theory for asymptotically cylindrical Calabi-Yau manifolds, similar to Koiso's approach [33] in the compact case.However, his parameter count is not entirely accurate, and he needs to assume an appropriate analog of the Tian-Todorov theorem [51,55], which seems to be still unknown; cf.Corollary 4.3.”
From Gravitational instantons from rational elliptic surfaces (2011) · cites this paper as [33]
The deformations of the flat metric on C^2/Λ, including a scale, are naturally identified with GL(3,R)/O(3).
“Hence, the deformations of the flat metric on C 2 /Λ, including a scale, are naturally identified with GL(3, R)/O(3).”
From Gravitational instantons from rational elliptic surfaces (2011) · cites this paper as [33]
Cites
Bott, R. (1957) · The Annals of Mathematics · doi:10.2307/1969996 · Cited by 714 · see citing works
On Deformations of Complex Analytic Structures, I
Kodaira, K., & Spencer, D. C. (1958) · The Annals of Mathematics · doi:10.2307/1970009 · Cited by 347 · see citing works
On Deformations of Complex Analytic Structures, III. Stability Theorems for Complex Structures
Kodaira, K., & Spencer, D. C. (1960) · The Annals of Mathematics · doi:10.2307/1969879 · Cited by 208 · see citing works
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Gravitational instantons from rational elliptic surfaces
Hein, H.-J. (2011) · Journal of the American Mathematical Society · doi:10.1090/s0894-0347-2011-00723-6 · Cited by 87 · see citing works
- Authors
- Koiso, N.
- Affiliations
- The University of Osaka (JP)
- Corresponding author
- Koiso, N.
- Venue
- Inventiones Mathematicae
- Published
- 1983-02
- Volume
- 73
- Issue
- 1
- Pages
- 71-106
- ISSN
- 0020-9910 (ISSN-L)
- 1432-1297
- OpenAlex
- W2068500992
- Cited by
- 106
- References
- 3
- Citations by year
- 2026: 2 · 2025: 4 · 2024: 3 · 2023: 6 · 2022: 7 · 2021: 4 · 2020: 8 · 2019: 1 · 2018: 4 · 2017: 3 · 2016: 2 · 2015: 3 · 2014: 7 · 2013: 6 · 2012: 2
- FWCI
- 4.60
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Inventiones mathematicae (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Geometry and Topology › Geometry and complex manifolds
- Physical Sciences › Mathematics › Geometry and Topology › Algebraic Geometry and Number Theory
- Physical Sciences › Mathematics › Applied Mathematics › Geometric Analysis and Curvature Flows
- Keywords
- Einstein metrics, complex structure, Ricci curvature, Kähler manifolds, conformal deformation
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