Weil Petersson Metric On The Universal Teichmuller Space
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Weil Petersson Metric On The Universal Teichmuller Space
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Author : Leon Armenovich Takhtadzhi︠a︡n
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Weil Petersson Metric On The Universal Teichmuller Space written by Leon Armenovich Takhtadzhi︠a︡n and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
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).
On Potential Funtion For The Weil Petersson Metric On Teichm Ller Space
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Author : Anthony J. Tromba
language : en
Publisher:
Release Date : 1987
On Potential Funtion For The Weil Petersson Metric On Teichm Ller Space written by Anthony J. Tromba and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with categories.
On The Weil Petersson Metric On Teichm Ller Space
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Author : Arthur E. Fischer
language : en
Publisher:
Release Date : 1982
On The Weil Petersson Metric On Teichm Ller Space written by Arthur E. Fischer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with categories.
An Introduction To Teichm Ller Spaces
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Author : Yoichi Imayoshi
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
An Introduction To Teichm Ller Spaces written by Yoichi Imayoshi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book offers an easy and compact access to the theory of TeichmA1/4ller spaces, starting from the most elementary aspects to the most recent developments, e.g. the role this theory plays with regard to string theory. TeichmA1/4ller spaces give parametrization of all the complex structures on a given Riemann surface. This subject is related to many different areas of mathematics including complex analysis, algebraic geometry, differential geometry, topology in two and three dimensions, Kleinian and Fuchsian groups, automorphic forms, complex dynamics, and ergodic theory. Recently, TeichmA1/4ller spaces have begun to play an important role in string theory. Imayoshi and Taniguchi have attempted to make the book as self-contained as possible. They present numerous examples and heuristic arguments in order to help the reader grasp the ideas of TeichmA1/4ller theory. The book will be an excellent source of information for graduate students and reserachers in complex analysis and algebraic geometry as well as for theoretical physicists working in quantum theory.
On A Potential Function For The Weil Petersson Metric On Teichm Ller Space
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Author : A. J. Tromba
language : de
Publisher:
Release Date : 1987
On A Potential Function For The Weil Petersson Metric On Teichm Ller Space written by A. J. Tromba and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with categories.
On A Potential Function For The Weil Petersson Metric On Teichm Ller Space
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Author : Anthony J. Tromba
language : en
Publisher:
Release Date : 1987
On A Potential Function For The Weil Petersson Metric On Teichm Ller Space written by Anthony J. Tromba and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with categories.
On The Weil Petersson Metric On Teichmueller Space
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Author : Arthur E. Fischer
language : en
Publisher:
Release Date : 1982
On The Weil Petersson Metric On Teichmueller Space written by Arthur E. Fischer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with categories.
Applications Of Calabi Yau Metric To The Weil Petersson Metric And The Teichm Ller Space Of Complex Manifold With C1 Iden 0
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Author : Andrey N. Todorov
language : de
Publisher:
Release Date : 1986
Applications Of Calabi Yau Metric To The Weil Petersson Metric And The Teichm Ller Space Of Complex Manifold With C1 Iden 0 written by Andrey N. Todorov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with categories.
Problems On Mapping Class Groups And Related Topics
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Author : Benson Farb
language : en
Publisher: American Mathematical Soc.
Release Date : 2006-09-12
Problems On Mapping Class Groups And Related Topics written by Benson Farb and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-12 with Mathematics categories.
The appearance of mapping class groups in mathematics is ubiquitous. The book presents 23 papers containing problems about mapping class groups, the moduli space of Riemann surfaces, Teichmuller geometry, and related areas. Each paper focusses completely on open problems and directions. The problems range in scope from specific computations, to broad programs. The goal is to have a rich source of problems which have been formulated explicitly and accessibly. The book is divided into four parts. Part I contains problems on the combinatorial and (co)homological group-theoretic aspects of mapping class groups, and the way in which these relate to problems in geometry and topology. Part II concentrates on connections with classification problems in 3-manifold theory, the theory of symplectic 4-manifolds, and algebraic geometry. A wide variety of problems, from understanding billiard trajectories to the classification of Kleinian groups, can be reduced to differential and synthetic geometry problems about moduli space. Such problems and connections are discussed in Part III. Mapping class groups are related, both concretely and philosophically, to a number of other groups, such as braid groups, lattices in semisimple Lie groups, and automorphism groups of free groups. Part IV concentrates on problems surrounding these relationships. This book should be of interest to anyone studying geometry, topology, algebraic geometry or infinite groups. It is meant to provide inspiration for everyone from graduate students to senior researchers.
In The Tradition Of Thurston Iii
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Author : Ken’ichi Ohshika
language : en
Publisher: Springer Nature
Release Date :
In The Tradition Of Thurston Iii written by Ken’ichi Ohshika and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.