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Complex Analytic Coordinates in Almost Complex Manifolds
Abstract
A manifold is called a complex manifold if it can be covered by coordinate patches with complex coordinates in which the coordinates in overlapping patches are related by complex analytic transformations. On such a manifold scalar multiplication by i in the tangent space has an invariant meaning. An even dimensional 2n real manifold is called almost complex if there is a linear transformation J defined on the tangent space at every point (and varying differentiably with respect to local coordinates) whose square is minus the identity, i.e. if there is a real tensor field h' satisfying
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Citations
Cited by
Irrationality and the $h$-cobordism conjecture
Donaldson, S. K. (1987) · Journal of Differential Geometry · doi:10.4310/jdg/1214441179 · Cited by 271
Chern, S. S. (1966) · Bulletin of the American Mathematical Society · doi:10.1090/s0002-9904-1966-11473-8 · Cited by 159
Metadata
- Authors
- Newlander, A., & Nirenberg, L.
- Venue
- The Annals of Mathematics
- Publisher
- JSTOR
- Published
- 1957-05
- Volume
- 65
- Issue
- 3
- Pages
- 391
- ISSN
- 0003-486X (ISSN-L)
- OpenAlex
- W2335103288
- Cited by
- 735
- References
- 0
- FWCI
- 8.96
- Type
- journal article
- Language
- en
- Open access
- closed
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- Newlander, A., & Nirenberg, L. (1957). Complex Analytic Coordinates in Almost Complex Manifolds. The Annals of Mathematics. https://doi.org/10.2307/1970051
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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.
