Riemannian Submersions And Related Topics

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Riemannian Submersions And Related Topics

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Author : Anna Maria Pastore
language : en
Publisher: World Scientific
Release Date : 2004-06-21

Riemannian Submersions And Related Topics written by Anna Maria Pastore and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-21 with Mathematics categories.

This book provides the first-ever systematic introduction to the theory of Riemannian submersions, which was initiated by Barrett O'Neill and Alfred Gray less than four decades ago. The authors focus their attention on classification theorems when the total space and the fibres have nice geometric properties. Particular emphasis is placed on the interrelation with almost Hermitian, almost contact and quaternionic geometry. Examples clarifying and motivating the theory are included in every chapter. Recent results on semi-Riemannian submersions are also explained. Finally, the authors point out the close connection of the subject with some areas of physics.

Riemannian Submersions And Related Topics

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Author : Maria Falcitelli
language : en
Publisher: World Scientific
Release Date : 2004

Riemannian Submersions And Related Topics written by Maria Falcitelli and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.

- First systematic exposition devoted to Riemannian submersions - Deals with current material - Contains a wide-ranging bibliography and about 350 references

Riemannian Submersions And Related Topics

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Author : Maria Falcitelli
language : en
Publisher: World Scientific
Release Date : 2004

Riemannian Submersions And Related Topics written by Maria Falcitelli and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.

This book provides the first-ever systematic introduction to thetheory of Riemannian submersions, which was initiated by BarrettO''Neill and Alfred Gray less than four decades ago. The authorsfocus their attention on classification theorems when the total spaceand the fibres have nice geometric properties.

Riemannian Submersions Riemannian Maps In Hermitian Geometry And Their Applications

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Author : Bayram Sahin
language : en
Publisher: Academic Press
Release Date : 2017-01-23

Riemannian Submersions Riemannian Maps In Hermitian Geometry And Their Applications written by Bayram Sahin and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-23 with Mathematics categories.

Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and their Applications is a rich and self-contained exposition of recent developments in Riemannian submersions and maps relevant to complex geometry, focusing particularly on novel submersions, Hermitian manifolds, and K\{a}hlerian manifolds. Riemannian submersions have long been an effective tool to obtain new manifolds and compare certain manifolds within differential geometry. For complex cases, only holomorphic submersions function appropriately, as discussed at length in Falcitelli, Ianus and Pastore's classic 2004 book. In this new book, Bayram Sahin extends the scope of complex cases with wholly new submersion types, including Anti-invariant submersions, Semi-invariant submersions, slant submersions, and Pointwise slant submersions, also extending their use in Riemannian maps. The work obtains new properties of the domain and target manifolds and investigates the harmonicity and geodesicity conditions for such maps. It also relates these maps with discoveries in pseudo-harmonic maps. Results included in this volume should stimulate future research on Riemannian submersions and Riemannian maps. - Systematically reviews and references modern literature in Riemannian maps - Provides rigorous mathematical theory with applications - Presented in an accessible reading style with motivating examples that help the reader rapidly progress

Harmonic Morphisms Harmonic Maps And Related Topics

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Author : Christopher Kum Anand
language : en
Publisher: CRC Press
Release Date : 1999-10-13

Harmonic Morphisms Harmonic Maps And Related Topics written by Christopher Kum Anand and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-10-13 with Mathematics categories.

The subject of harmonic morphisms is relatively new but has attracted a huge worldwide following. Mathematicians, young researchers and distinguished experts came from all corners of the globe to the City of Brest - site of the first, international conference devoted to the fledgling but dynamic field of harmonic morphisms. Harmonic Morphisms, Harmonic Maps, and Related Topics reports the proceedings of that conference, forms the first work primarily devoted to harmonic morphisms, bringing together contributions from the founders of the subject, leading specialists, and experts in other related fields. Starting with "The Beginnings of Harmonic Morphisms," which provides the essential background, the first section includes papers on the stability of harmonic morphisms, global properties, harmonic polynomial morphisms, Bochner technique, f-structures, symplectic harmonic morphisms, and discrete harmonic morphisms. The second section addresses the wider domain of harmonic maps and contains some of the most recent results on harmonic maps and surfaces. The final section highlights the rapidly developing subject of constant mean curvature surfaces. Harmonic Morphisms, Harmonic Maps, and Related Topics offers a coherent, balanced account of this fast-growing subject that furnishes a vital reference for anyone working in the field.

Complex Geometry Of Slant Submanifolds

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Author : Bang-Yen Chen
language : en
Publisher: Springer Nature
Release Date : 2022-05-11

Complex Geometry Of Slant Submanifolds written by Bang-Yen Chen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-11 with Mathematics categories.

This book contains an up-to-date survey and self-contained chapters on complex slant submanifolds and geometry, authored by internationally renowned researchers. The book discusses a wide range of topics, including slant surfaces, slant submersions, nearly Kaehler, locally conformal Kaehler, and quaternion Kaehler manifolds. It provides several classification results of minimal slant surfaces, quasi-minimal slant surfaces, slant surfaces with parallel mean curvature vector, pseudo-umbilical slant surfaces, and biharmonic and quasi biharmonic slant surfaces in Lorentzian complex space forms. Furthermore, this book includes new results on slant submanifolds of para-Hermitian manifolds. This book also includes recent results on slant lightlike submanifolds of indefinite Hermitian manifolds, which are of extensive use in general theory of relativity and potential applications in radiation and electromagnetic fields. Various open problems and conjectures on slant surfaces in complex space forms are also included in the book. It presents detailed information on the most recent advances in the area, making it valuable for scientists, educators and graduate students.

Einstein Manifolds

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Author : Arthur L. Besse
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-03

Einstein Manifolds written by Arthur L. Besse 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 2007-12-03 with Mathematics categories.

Einstein's equations stem from General Relativity. In the context of Riemannian manifolds, an independent mathematical theory has developed around them. This is the first book which presents an overview of several striking results ensuing from the examination of Einstein’s equations in the context of Riemannian manifolds. Parts of the text can be used as an introduction to modern Riemannian geometry through topics like homogeneous spaces, submersions, or Riemannian functionals.

Riemannian Geometry

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Author : Peter Petersen
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-11-24

Riemannian Geometry written by Peter Petersen 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 2006-11-24 with Mathematics categories.

This volume introduces techniques and theorems of Riemannian geometry, and opens the way to advanced topics. The text combines the geometric parts of Riemannian geometry with analytic aspects of the theory, and reviews recent research. The updated second edition includes a new coordinate-free formula that is easily remembered (the Koszul formula in disguise); an expanded number of coordinate calculations of connection and curvature; general fomulas for curvature on Lie Groups and submersions; variational calculus integrated into the text, allowing for an early treatment of the Sphere theorem using a forgotten proof by Berger; recent results regarding manifolds with positive curvature.

Riemannian Manifolds And Homogeneous Geodesics

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Author : Valerii Berestovskii
language : en
Publisher: Springer Nature
Release Date : 2020-11-05

Riemannian Manifolds And Homogeneous Geodesics written by Valerii Berestovskii and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-05 with Mathematics categories.

This book is devoted to Killing vector fields and the one-parameter isometry groups of Riemannian manifolds generated by them. It also provides a detailed introduction to homogeneous geodesics, that is, geodesics that are integral curves of Killing vector fields, presenting both classical and modern results, some very recent, many of which are due to the authors. The main focus is on the class of Riemannian manifolds with homogeneous geodesics and on some of its important subclasses. To keep the exposition self-contained the book also includes useful general results not only on geodesic orbit manifolds, but also on smooth and Riemannian manifolds, Lie groups and Lie algebras, homogeneous Riemannian manifolds, and compact homogeneous Riemannian spaces. The intended audience is graduate students and researchers whose work involves differential geometry and transformation groups.

Geometry Of Cauchy Riemann Submanifolds

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Author : Sorin Dragomir
language : en
Publisher: Springer
Release Date : 2016-05-31

Geometry Of Cauchy Riemann Submanifolds written by Sorin Dragomir and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-31 with Mathematics categories.

This book gathers contributions by respected experts on the theory of isometric immersions between Riemannian manifolds, and focuses on the geometry of CR structures on submanifolds in Hermitian manifolds. CR structures are a bundle theoretic recast of the tangential Cauchy–Riemann equations in complex analysis involving several complex variables. The book covers a wide range of topics such as Sasakian geometry, Kaehler and locally conformal Kaehler geometry, the tangential CR equations, Lorentzian geometry, holomorphic statistical manifolds, and paraquaternionic CR submanifolds. Intended as a tribute to Professor Aurel Bejancu, who discovered the notion of a CR submanifold of a Hermitian manifold in 1978, the book provides an up-to-date overview of several topics in the geometry of CR submanifolds. Presenting detailed information on the most recent advances in the area, it represents a useful resource for mathematicians and physicists alike.