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.
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Editorial Reviews
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The reader should have little difficulty in locating the many different concepts in this rich and rewarding text. Young geometers looking for problems and more importantly directions for future work will find reading this book provides a fine source of material and papers. -- Mathematical Reviews
This is a very well-written and interesting book on Riemannian submersions and it is the first monograph in the literature about this topic. -- Zentralblatt MATH
Well written, gathering information spread in a lot of papers, unifying the style of many authors, with most of the proofs carried in all details, with a wealth of examples, it certainly fills a gap in the literature and will be a prior reference for both researchers and students. -- Romanian Journal of Pure and Applied Mathematics
This is a very well-written and interesting book on Riemannian submersions and it is the first monograph in the literature about this topic. -- Zentralblatt MATH
Well written, gathering information spread in a lot of papers, unifying the style of many authors, with most of the proofs carried in all details, with a wealth of examples, it certainly fills a gap in the literature and will be a prior reference for both researchers and students. -- Romanian Journal of Pure and Applied Mathematics
Review
This is a very well-written and interesting book on Riemannian submersions and it is the first monograph in the literature about this topic.
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Inside This Book
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First Sentence:
Let (M, g) and (B, g1) be C -Riemannian manifolds of dimension m and n, respectively. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
geodesic fibres, umbilical fibres, fibres isometric, integrability tensor, conformal submersions, basic vector fields, mean curvature vector field, minimal fibres, canonical fibration, principal torus, canonical variation, integrable horizontal distribution, constant holomorphic sectional curvature, holomorphic sectional curvatures, principal circle bundle, codifferential operator, whose total space, horizontal vector fields, bisectional curvatures, vertical vector fields, holomorphic submanifolds, isometric immersion, warped product, characteristic vector field, harmonic morphisms Key Phrases - Capitalized Phrases (CAPs): (learn more)
G-invariant Einstein, Hermitian Einstein-Weyl New!
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Let (M, g) and (B, g1) be C -Riemannian manifolds of dimension m and n, respectively. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
geodesic fibres, umbilical fibres, fibres isometric, integrability tensor, conformal submersions, basic vector fields, mean curvature vector field, minimal fibres, canonical fibration, principal torus, canonical variation, integrable horizontal distribution, constant holomorphic sectional curvature, holomorphic sectional curvatures, principal circle bundle, codifferential operator, whose total space, horizontal vector fields, bisectional curvatures, vertical vector fields, holomorphic submanifolds, isometric immersion, warped product, characteristic vector field, harmonic morphisms Key Phrases - Capitalized Phrases (CAPs): (learn more)
G-invariant Einstein, Hermitian Einstein-Weyl New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 10
books:
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- Surveys in Differential Geometry, Vol. 6: Essays on Einstein Manifolds by Claude LeBrun in Back Matter
- Foliations on Riemannian Manifolds (Universitext) by Philippe Tondeur in Back Matter
- Riemannian Geometry (De Gruyter Studies in Mathematics) by Wilhelm P. A. Klingenberg in Back Matter
- Topics in Differential Geometry by J. Szenthe in Back Matter
- Superstring Theory: Volume 2, Loop Amplitudes, Anomalies and Phenomenology (Cambridge Monographs on Mathematical Physics) by Michael B. Green in Back Matter
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