On the Positive Holomorphic Sectional Curvature of Projectivized Vector Bundles Over Compact Complex Manifolds PDF Download
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Author: Angelynn Reario Alvarez
Publisher:
ISBN:
Category : Complex manifolds
Languages : en
Pages :
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Book Description
In complex geometry, there are few known examples of, and few known results about, manifolds with metrics of positive curvature. For instance, the geometry of fiber bundles and total spaces of fibrations over positively-curved complex manifolds is mysterious and not well-understood. In this dissertation, we study the existence of (pinched) metrics of positive curvature on a particular type of fiber bundle---namely metrics of positive holomorphic sectional curvature on projectivized vector bundles over compact complex manifolds. We first prove a general theorem for projectivized vector bundles, then we discuss a curvature pinching result for projectivized rank 2 vector bundles over complex projective space of dimension 1.
Author: Angelynn Reario Alvarez
Publisher:
ISBN:
Category : Complex manifolds
Languages : en
Pages :
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Book Description
In complex geometry, there are few known examples of, and few known results about, manifolds with metrics of positive curvature. For instance, the geometry of fiber bundles and total spaces of fibrations over positively-curved complex manifolds is mysterious and not well-understood. In this dissertation, we study the existence of (pinched) metrics of positive curvature on a particular type of fiber bundle---namely metrics of positive holomorphic sectional curvature on projectivized vector bundles over compact complex manifolds. We first prove a general theorem for projectivized vector bundles, then we discuss a curvature pinching result for projectivized rank 2 vector bundles over complex projective space of dimension 1.
Author: Vasile Brinzanescu
Publisher: Springer
ISBN: 3540498451
Category : Mathematics
Languages : en
Pages : 175
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Book Description
The purpose of this book is to present the available (sometimes only partial) solutions to the two fundamental problems: the existence problem and the classification problem for holomorphic structures in a given topological vector bundle over a compact complex surface. Special features of the nonalgebraic surfaces case, like irreducible vector bundles and stability with respect to a Gauduchon metric, are considered. The reader requires a grounding in geometry at graduate student level. The book will be of interest to graduate students and researchers in complex, algebraic and differential geometry.
Author: S. Kobayashi
Publisher: Birkhäuser
ISBN: 303486566X
Category : Science
Languages : en
Pages : 159
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Book Description
Author: Shoshichi Kobayashi
Publisher: Princeton University Press
ISBN: 1400858682
Category : Mathematics
Languages : en
Pages : 317
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Book Description
Holomorphic vector bundles have become objects of interest not only to algebraic and differential geometers and complex analysts but also to low dimensional topologists and mathematical physicists working on gauge theory. This book, which grew out of the author's lectures and seminars in Berkeley and Japan, is written for researchers and graduate students in these various fields of mathematics. Originally published in 1987. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author: Vasile Brînzănescu
Publisher:
ISBN: 9780387610184
Category : Mathematics
Languages : en
Pages : 170
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Book Description
Author: Yanir A. Rubinstein
Publisher: American Mathematical Soc.
ISBN: 1470443333
Category : Geometry
Languages : en
Pages : 259
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Book Description
This volume contains contributions from speakers at the 2015–2018 joint Johns Hopkins University and University of Maryland Complex Geometry Seminar. It begins with a survey article on recent developments in pluripotential theory and its applications to Kähler–Einstein metrics and continues with articles devoted to various aspects of the theory of complex manifolds and functions on such manifolds.
Author: Jaume Amorós
Publisher: American Mathematical Soc.
ISBN: 0821804987
Category : Mathematics
Languages : en
Pages : 154
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Book Description
This book is an exposition of what is currently known about the fundamental groups of compact Kähler manifolds. This class of groups contains all finite groups and is strictly smaller than the class of all finitely presentable groups. For the first time ever, this book collects together all the results obtained in the last few years which aim to characterize those infinite groups which can arise as fundamental groups of compact Kähler manifolds. Most of these results are negative ones, saying which groups don not arise. The methods and techniques used form an attractive mix of topology, differential and algebraic geometry, and complex analysis. The book would be useful to researchers and graduate students interested in any of these areas, and it could be used as a textbook for an advanced graduate course. One of its outstanding features is a large number of concrete examples. The book contains a number of new results and examples which have not appeared elsewhere, as well as discussions of some important open questions in the field.
Author: Werner Ballmann
Publisher: European Mathematical Society
ISBN: 9783037190258
Category : Mathematics
Languages : en
Pages : 190
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Book Description
These notes are based on lectures the author gave at the University of Bonn and the Erwin Schrodinger Institute in Vienna. The aim is to give a thorough introduction to the theory of Kahler manifolds with special emphasis on the differential geometric side of Kahler geometry. The exposition starts with a short discussion of complex manifolds and holomorphic vector bundles and a detailed account of the basic differential geometric properties of Kahler manifolds. The more advanced topics are the cohomology of Kahler manifolds, Calabi conjecture, Gromov's Kahler hyperbolic spaces, and the Kodaira embedding theorem. Some familiarity with global analysis and partial differential equations is assumed, in particular in the part on the Calabi conjecture. There are appendices on Chern-Weil theory, symmetric spaces, and $L^2$-cohomology.
Author: Chen-Han Sung
Publisher:
ISBN:
Category :
Languages : en
Pages : 164
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Book Description
Author: Chi Keung Cheung
Publisher:
ISBN:
Category :
Languages : en
Pages : 152
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Book Description
