Principles Of Locally Conformally K Hler Geometry
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Principles Of Locally Conformally K Hler Geometry
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Author : Liviu Ornea
language : en
Publisher: Springer Nature
Release Date : 2024-05-02
Principles Of Locally Conformally K Hler Geometry written by Liviu Ornea and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-02 with Mathematics categories.
This monograph introduces readers to locally conformally Kähler (LCK) geometry and provides an extensive overview of the most current results. A rapidly developing area in complex geometry dealing with non-Kähler manifolds, LCK geometry has strong links to many other areas of mathematics, including algebraic geometry, topology, and complex analysis. The authors emphasize these connections to create a unified and rigorous treatment of the subject suitable for both students and researchers. Part I builds the necessary foundations for those approaching LCK geometry for the first time with full, mostly self-contained proofs and also covers material often omitted from textbooks, such as contact and Sasakian geometry, orbifolds, Ehresmann connections, and foliation theory. More advanced topics are then treated in Part II, including non-Kähler elliptic surfaces, cohomology of holomorphic vector bundles on Hopf manifolds, Kuranishi and Teichmüller spaces for LCK manifolds with potential, and harmonic forms on Sasakian and Vaisman manifolds. Each chapter in Parts I and II begins with motivation and historic context for the topics explored and includes numerous exercises for further exploration of important topics. Part III surveys the current research on LCK geometry, describing advances on topics such as automorphism groups on LCK manifolds, twisted Hamiltonian actions and LCK reduction, Einstein-Weyl manifolds and the Futaki invariant, and LCK geometry on nilmanifolds and on solvmanifolds. New proofs of many results are given using the methods developed earlier in the text. The text then concludes with a chapter that gathers over 100 open problems, with context and remarks provided where possible, to inspire future research.
Essays On Topology
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Author : Louis Funar
language : en
Publisher: Springer Nature
Release Date : 2025-07-21
Essays On Topology written by Louis Funar and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-21 with Mathematics categories.
This book consists of a collection of articles dedicated to Valentin Poénaru, on topology and geometry in a broad sense. Poénaru is one of the leading mathematicians whose work had an essential impact on the development of topology in France over the last forty years of the twentieth century. The special topics addressed in this volume include hyperbolic geometry, 3-manifolds, complex and symplectic geometry, differential topology, combinatorial group theory, piecewise-linear topology, algebraic geometry, knots and links, homotopy theory, braid groups, phylogenetics, the history of geometry, and the philosophy of mathematics. This collection of articles, written by well-known researchers, provides a lively insight into a number of current research topics in geometry and topology.
Real And Complex Geometry
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Author : Liviu Ornea
language : en
Publisher: Springer Nature
Release Date : 2025-08-02
Real And Complex Geometry written by Liviu Ornea and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-08-02 with Mathematics categories.
The book covers a wide area of hot subjects in real and complex differential geometry, such as conformal geometry, special holonomy, Sasakian geometry, Kähler and non-Kähler metrics, classification of compact complex surfaces, Einstein metrics, bi-Hermitian geometry, non-integrable almost complex structures, etc. All of these are rather close to Paul Gauduchon’s themes and influential results in the past fifty years. The reader will find fifteen papers – a few surveys, but the majority containing new and exciting results. The book thus gives an idea of the present research interests of some of the best experts today in real and complex differential geometry including Vestislav Apostolov, Florin Belgun, Charles Boyer, Georges Dloussky, Anna Fino, Gueo Grantcharov, Claude LeBrun, Andrei Moroianu, Massimiliano Pontecorvo, Simon Salamon, Andrew Swann, Adriano Tomassini, Valentino Tosatti, and Misha Verbitsky.
The Geometry Of Higher Order Lagrange Spaces
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Author : R. Miron
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
The Geometry Of Higher Order Lagrange Spaces written by R. Miron 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 2013-11-11 with Mathematics categories.
This monograph is devoted to the problem of the geometrizing of Lagrangians which depend on higher-order accelerations. It presents a construction of the geometry of the total space of the bundle of the accelerations of order k>=1. A geometrical study of the notion of the higher-order Lagrange space is conducted, and the old problem of prolongation of Riemannian spaces to k-osculator manifolds is solved. Also, the geometrical ground for variational calculus on the integral of actions involving higher-order Lagrangians is dealt with. Applications to higher-order analytical mechanics and theoretical physics are included as well. Audience: This volume will be of interest to scientists whose work involves differential geometry, mechanics of particles and systems, calculus of variation and optimal control, optimization, optics, electromagnetic theory, and biology.
Algebraic Geometry
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Author :
language : en
Publisher:
Release Date : 2004
Algebraic Geometry written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Geometry, Algebraic categories.
Harmonic Vector Fields
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Author : Sorin Dragomir
language : en
Publisher: Elsevier
Release Date : 2012
Harmonic Vector Fields written by Sorin Dragomir and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Computers categories.
An excellent reference for anyone needing to examine properties of harmonic vector fields to help them solve research problems. The book provides the main results of harmonic vector ?elds with an emphasis on Riemannian manifolds using past and existing problems to assist you in analyzing and furnishing your own conclusion for further research. It emphasizes a combination of theoretical development with practical applications for a solid treatment of the subject useful to those new to research using differential geometric methods in extensive detail. A useful tool for any scientist conducting research in the field of harmonic analysis Provides applications and modern techniques to problem solving A clear and concise exposition of differential geometry of harmonic vector fields on Reimannian manifolds Physical Applications of Geometric Methods
Harmonic Morphisms Between Riemannian Manifolds
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Author : Paul Baird
language : en
Publisher: Oxford University Press
Release Date : 2003
Harmonic Morphisms Between Riemannian Manifolds written by Paul Baird and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
This is an account in book form of the theory of harmonic morphisms between Riemannian manifolds.
Encyclopaedia Of Mathematics
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Author : Michiel Hazewinkel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Encyclopaedia Of Mathematics written by Michiel Hazewinkel 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 is the second supplementary volume to Kluwer's highly acclaimed eleven-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing eleven volumes, and together these twelve volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.
New Symmetry Principles In Quantum Field Theory
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Author : J. Frölich
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
New Symmetry Principles In Quantum Field Theory written by J. Frölich 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 Science categories.
Soon after the discovery of quantum mechanics, group theoretical methods were used extensively in order to exploit rotational symmetry and classify atomic spectra. And until recently it was thought that symmetries in quantum mechanics should be groups. But it is not so. There are more general algebras, equipped with suitable structure, which admit a perfectly conventional interpretation as a symmetry of a quantum mechanical system. In any case, a "trivial representation" of the algebra is defined, and a tensor product of representations. But in contrast with groups, this tensor product needs to be neither commutative nor associative. Quantum groups are special cases, in which associativity is preserved. The exploitation of such "Quantum Symmetries" was a central theme at the Ad vanced Study Institute. Introductory lectures were presented to familiarize the participants with the al gebras which can appear as symmetries and with their properties. Some models of local field theories were discussed in detail which have some such symmetries, in par ticular conformal field theories and their perturbations. Lattice models provide many examples of quantum theories with quantum symmetries. They were also covered at the school. Finally, the symmetries which are the cause of the solubility of inte grable models are also quantum symmetries of this kind. Some such models and their nonlocal conserved currents were discussed.
Differential Geometry
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Author : L. A. Cordero
language : en
Publisher: Pitman Advanced Publishing Program
Release Date : 1985
Differential Geometry written by L. A. Cordero and has been published by Pitman Advanced Publishing Program this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mathematics categories.