Weil Petersson Metric on the Universal Teichmuller Space is popular PDF and ePub book, written by Leon Armenovich Takhtadzhi︠a︡n in 2006, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Weil Petersson Metric on the Universal Teichmuller Space can be Read Online from any device for your convenience.
Weil Petersson Metric on the Universal Teichmuller Space Book PDF Summary
In this memoir, we prove that the universal Teichmuller space $T(1)$ carries a new structure of a complex Hilbert manifold and show that the connected component of the identity of $T(1)$ -- the Hilbert submanifold $T {0 (1)$ -- is a topological group. We define a Weil-Petersson metric on $T(1)$ by Hilbert space inner products on tangent spaces, compute its Riemann curvature tensor, and show that $T(1)$ is a Kahler-Einstein manifold with negative Ricci and sectional curvatures. We introduce and compute Mumford-Miller-Morita characteristic forms for the vertical tangent bundle of the universal Teichmuller curve fibration over the universal Teichmuller space. As an application, we derive Wolpert curvature formulas for the finite-dimensional Teichmuller spaces from the formulas for the universal Teichmuller space. We study in detail the Hilbert manifold structure on $T {0 (1)$ and characterize points on $T {0 (1)$ in terms of Bers and pre-Bers embeddings by proving that the Grunsky operators $B {1 $ and The results of this memoir were presented in our e-prints: Weil-Petersson metric on the universal Teichmuller space I. Curvature properties and Chern forms, arXiv:math.CV/0312172 (2003), and Weil-Petersson metric on the universal Teichmuller space II. Kahler potential and period mapping, arXiv:math.CV/0406408 (2004).
Detail Book of Weil Petersson Metric on the Universal Teichmuller Space PDF
- Author : Leon Armenovich Takhtadzhi︠a︡n
- Release : 29 September 2024
- Publisher : American Mathematical Soc.
- ISBN : 9780821839362
- Genre : Mathematics
- Total Page : 136 pages
- Language : English
- PDF File Size : 20,9 Mb
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