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Elementary Symplectic Topology and Mechanics
This is a short tract on the essentials of differential and symplectic geometry together with a basic introduction to several applications of this rich framework: analytical mechanics, the calculus of variations, conjugate points & Morse index, and other physical topics. A central feature is the systematic utilization of Lagrangian submanifolds and their Maslov-Hörmander generating functions. …
- Edition
- 1
- ISBN/ISSN
- 978-3-319-11026-4
- Collation
- 33 b/w illustrations, 11 illustrations in colour
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- -
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Hyperbolicity of Projective Hypersurfaces
This book presents recent advances on Kobayashi hyperbolicity in complex geometry, especially in connection with projective hypersurfaces. This is a very active field, not least because of the fascinating relations with complex algebraic and arithmetic geometry. Foundational works of Serge Lang and Paul A. Vojta, among others, resulted in precise conjectures regarding the interplay of these res…
- Edition
- -
- ISBN/ISSN
- 978-3-319-32314-5
- Collation
- XIV, 89
- Series Title
- -
- Call Number
- 510 DIV h
Conformal Symmetry Breaking Operators for Differential Forms on Spheres
This work is the first systematic study of all possible conformally covariant differential operators transforming differential forms on a Riemannian manifold X into those on a submanifold Y with focus on the model space (X, Y) = (Sn, Sn-1). The authors give a complete classification of all such conformally covariant differential operators, and find their explicit formulæ in the flat coordinate…
- Edition
- 1
- ISBN/ISSN
- 9789811026577
- Collation
- ix, 192 pages
- Series Title
- Lecture Notes in Mathematics
- Call Number
- 516.36
Riemannian Geometry
Intended for a one year course, this text serves as a single source, introducing readers to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few Works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory. The …
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Ricci Flow and Geometric Applications
Presenting some impressive recent achievements in differential geometry and topology, this volume focuses on results obtained using techniques based on Ricci flow. These ideas are at the core of the study of differentiable manifolds. Several very important open problems and conjectures come from this area and the techniques described herein are used to face and solve some of them. The bookâ…
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- Ed. 1
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- -
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Information Geometry and Its Applications
This is the first comprehensive book on information geometry, written by the founder of the field. It begins with an elementary introduction to dualistic geometry and proceeds to a wide range of applications, covering information science, engineering, and neuroscience. It consists of four parts, which on the whole can be read independently. A manifold with a divergence function is first introdu…
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- ISBN/ISSN
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- Collation
- XIII, 374
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- Call Number
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Theory of Control Systems Described by Differential Inclusions
This book provides a brief introduction to the theory of finite dimensional differential inclusions, and deals in depth with control of three kinds of differential inclusion systems. The authors introduce the algebraic decomposition of convex processes, the stabilization of polytopic systems, and observations of Luré systems. They also introduce the elemental theory of finite dimensional diffe…
- Edition
- -
- ISBN/ISSN
- 978-3-662-49245-1
- Collation
- -
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- Call Number
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An Invitation to Web Geometry
This book takes an in-depth look at abelian relations of codimension one webs in the complex analytic setting. In its classical form, web geometry consists in the study of webs up to local diffeomorphisms. A significant part of the theory revolves around the concept of abelian relation, a particular kind of functional relation among the first integrals of the foliations of a web. Two main focus…
- Edition
- Ed. 1
- ISBN/ISSN
- 978-3-319-14562-4
- Collation
- XVII, 213
- Series Title
- IMPA Monographs
- Call Number
- 515.3 PER i
An Introduction to Differential Manifolds
This book is an introduction to differential manifolds. It gives solid preliminaries for more advanced topics: Riemannian manifolds, differential topology, Lie theory. It presupposes little background: the reader is only expected to master basic differential calculus, and a little point-set topology. The book covers the main topics of differential geometry: manifolds, tangent space, vector fiel…
- Edition
- Ed. 1
- ISBN/ISSN
- 978-3-319-20735-3
- Collation
- XIX, 395
- Series Title
- -
- Call Number
- 516 LAF i
L² Approaches in Several Complex Variables: Development of Oka–Cartan Theo…
The purpose of this monograph is to present the current status of a rapidly developing part of several complex variables, motivated by the applicability of effective results to algebraic geometry and differential geometry. Highlighted are the new precise results on the L² extension of holomorphic functions. In Chapter 1, the classical questions of several complex variables motivating the de…
- Edition
- -
- ISBN/ISSN
- 978-4-431-55747-0
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- -
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