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Cited by 15

The DOI matches its Crossref record; 16 of the 16 references it cites were found in a registry or an index.

MODULI SPACES OF TOPOLOGICAL CALIBRATIONS, CALABI–YAU, HYPERKÄHLER, G2and SPIN(7) STRUCTURES

GOTO, RYUSHI·2004·International Journal of Mathematics
DOI 10.1142/s0129167x04002296
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Abstract

This paper focuses on a geometric structure defined by a system of closed exterior differential forms and develops a new approach to deformation problems of geometric structures. We obtain a criterion for unobstructed deformations from a cohomological point of view (Theorem 1.7). Further we show that under a cohomological condition, the moduli space of the geometric structures becomes a smooth manifold of finite dimension (Theorem 1.8). We apply our approach to the geometric structures such as Calabi–Yau, HyperKähler, G 2 and Spin(7) structures and then obtain a unified construction of smooth moduli spaces of these four geometric structures. We generalize the Moser's stability theorem to provide a direct proof of the local Torelli type theorem in these four geometric structures (Theorem 1.10).

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Crossref · 10.1142/s0129167x04002296

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16 of 16 references verified0 citation errors · 0 not checkable

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Citations

Cites

Research works printed but not linked: 12

  1. Besse A. L., Einstein Manifolds, 10
  2. Bogomolov F. A., Dolk. Akad. Nauk SSSR, 243, 1101
  3. Gilky P. B., 1984, Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem, 11
  4. Harvey F. R., 1990, Spinors and Calibrations, 9
  5. Joyce D. D., Invent. Math., 128, 507
  6. Kawamata Y., J. Algebraic Geom., 1, 183
  7. Kobayashi S., 1969, Foundation of Differential Geometry I, II
  8. Lawson H. B., 1989, Spin Geometry
  9. Omori H., Infinite Dimensional Lie Group, 158
  10. Palais R. S., 1968, Foundations of Non-Linear Functional Analysis
  11. Salamon S., 1989, Riemannian Geometry and Holonomy Groups, 201
  12. G. Tian, Essays on Mirror Manifolds (International Press, 1992) pp. 458–479.

Cited by

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Metadata

Authors
GOTO, R.
Affiliations
Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka, 560, Japan
Venue
International Journal of Mathematics
Publisher
World Scientific Pub Co Pte Ltd
Published
2004-05
Volume
15
Issue
03
Pages
211-257
ISSN
  • 0129-167X
  • 1793-6519
DOI
10.1142/s0129167x04002296
Cited by
15
References
16
Language
en

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Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.