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Foliations On Riemannian Manifolds (Universitext)
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A First Approximation To The Idea Of A Foliation Is A Dynamical System, And The Resulting Decomposition Of A Domain By Its Trajectories. This Is An Idea That Dates Back To The Beginning Of The Theory Of Differential Equations, I.E. The Seventeenth Century. Towards The End Of The Nineteenth Century, Poincare Developed Methods For The Study Of Global, Qualitative Properties Of Solutions Of Dynamical Systems In Situations Where Explicit Solution Methods Had Failed: He Discovered That The Study Of The Geometry Of The Space Of Trajectories Of A Dynamical System Reveals Complex Phenomena. He Emphasized The Qualitative Nature Of These Phenomena, Thereby Giving Strong Impetus To Topological Methods. A Second Approximation Is The Idea Of A Foliation As A Decomposition Of A Manifold Into Submanifolds, All Being Of The Same Dimension. Here The Presence Of Singular Submanifolds, Corresponding To The Singularities In The Case Of A Dynamical System, Is Excluded. This Is The Case We Treat In This Text, But It Is By No Means A Comprehensive Analysis. On The Contrary, Many Situations In Mathematical Physics Most Definitely Require Singular Foliations For A Proper Modeling. The Global Study Of Foliations In The Spirit Of Poincare Was Begun Only In The 1940'S, By Ehresmann And Reeb.
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- Q: How many pages are in 'Foliations on Riemannian Manifolds'? A: There are two hundred fifty-eight pages in this book. This length provides a thorough exploration of the subject matter.
- Q: What are the dimensions of this book? A: The book measures six point one inches long, zero point five nine inches wide, and nine point twenty-five inches tall. These dimensions make it portable and easy to handle.
- Q: What type of binding does this book have? A: This book is available in paperback binding. This makes it flexible and lightweight for easy reading.
- Q: Who is the author of 'Foliations on Riemannian Manifolds'? A: The author is Philippe Tondeur. He brings expertise in differential geometry to this text.
- Q: What category does this book fall under? A: The book is categorized under Differential Geometry. This genre focuses on the geometric properties and structures of differentiable manifolds.
- Q: What is the main topic of this book? A: The main topic is the study of foliations on Riemannian manifolds. It explores the decomposition of manifolds into submanifolds.
- Q: Is this book suitable for beginners? A: Yes, this book is suitable for those with a basic understanding of differential equations. It introduces complex concepts in a digestible manner.
- Q: Who would benefit from reading this book? A: Students and professionals in mathematics or physics would benefit greatly. The book addresses both foundational and advanced topics in the field.
- Q: What concepts are covered in this book? A: The book covers dynamical systems, global properties of solutions, and qualitative phenomena in geometry. It provides insights into both singular and non-singular foliations.
- Q: How should I store this book? A: Store this book in a cool, dry place to preserve its condition. Avoid direct sunlight to prevent fading of the cover and pages.
- Q: Is this book safe for all audiences? A: Yes, this book is appropriate for academic audiences and does not contain adult content. It is focused on mathematical concepts.
- Q: How do I clean this book if it gets dirty? A: To clean this book, gently wipe the cover with a soft, dry cloth. Avoid using water or cleaning solutions that could damage the binding.
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- Q: Does this book include illustrations or diagrams? A: Yes, the book includes diagrams to illustrate complex concepts. These visual aids enhance understanding of the material.