A period mapping in universal Teichmüller space
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- by Subhashis Nag PDF
- Bull. Amer. Math. Soc. 26 (1992), 280-287 Request permission
Abstract:
In previous work it had been shown that the remarkable homogeneous space $M = \operatorname {Diff}({S^1})/{\text {PSL}}(2,\mathbb {R})$ sits as a complex analytic and Kähler submanifold of the Universal Teichmüller Space. There is a natural immersion $\prod$ of M into the infinite-dimensional version (due to Segal) of the Siegel space of period matrices. That map $\prod$ is proved to be injective, equivariant, holomorphic, and Kähler-isometric (with respect to the canonical metrics). Regarding a period mapping as a map describing the variation of complex structure, we explain why $\prod$ is an infinite-dimensional period mapping.References
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Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Bull. Amer. Math. Soc. 26 (1992), 280-287
- MSC (2000): Primary 32G20; Secondary 30F60, 32G15, 81S10, 81T30
- DOI: https://doi.org/10.1090/S0273-0979-1992-00273-2
- MathSciNet review: 1121571