Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On the Weil-Petersson metric on Teichmüller space

Authors: A. E. Fischer and A. J. Tromba
Journal: Trans. Amer. Math. Soc. 284 (1984), 319-335
MSC: Primary 32G15; Secondary 58B20
MathSciNet review: 742427
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Teichmüller space for a compact oriented surface $ M$ without boundary is described as the quotient $ \mathcal{A}/{\mathcal{D}_0}$, where $ \mathcal{A}$ is the space of almost complex structures on $ M$ (compatible with a given orientation) and $ {\mathcal{D}_0}$ are those $ {C^\infty }$ diffeomorphisms homotopic to the identity. There is a natural $ {\mathcal{D}_0}$ invariant $ {L_2}$ Riemannian structure on $ \mathcal{A}$ which induces a Riemannian structure on $ \mathcal{A}/{\mathcal{D}_0}$. Infinitesimally this is the bilinear pairing suggested by Andre Weil--the Weil-Petersson Riemannian structure. The structure is shown to be Kähler with respect to a naturally induced complex structure on $ \mathcal{A}/{\mathcal{D}_0}$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 32G15, 58B20

Retrieve articles in all journals with MSC: 32G15, 58B20

Additional Information

Article copyright: © Copyright 1984 American Mathematical Society

American Mathematical Society