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Riemannian Manifolds

An Introduction to Curvature

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Focusing on the geometric meaning of curvature, this textbook for graduate students emphasizes essential tools for studying Riemannian geometry. It covers metrics, connections, and geodesics before introducing the Riemann curvature tensor and submanifold theory for practical interpretation. The text aims to prove four fundamental theorems linking curvature and topology, including the Gauss-Bonnet and Cartan-Hadamard theorems. Selected topics are structured for a concise ten to fifteen-week course, prioritizing depth over breadth in the subject matter.

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Riemannian Manifolds, John Lee

Taal
Jaar van publicatie
1997
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(Hardcover)
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Titel
Riemannian Manifolds
Ondertitel
An Introduction to Curvature
Taal
Engels
Auteurs
John Lee
Jaar van publicatie
1997
Formaat
Hardcover
Aantal pagina's
226
ISBN13
9780387982717
Reeks
Beoordeling
4,5 van 5
Aantekening
Focusing on the geometric meaning of curvature, this textbook for graduate students emphasizes essential tools for studying Riemannian geometry. It covers metrics, connections, and geodesics before introducing the Riemann curvature tensor and submanifold theory for practical interpretation. The text aims to prove four fundamental theorems linking curvature and topology, including the Gauss-Bonnet and Cartan-Hadamard theorems. Selected topics are structured for a concise ten to fifteen-week course, prioritizing depth over breadth in the subject matter.