Introduction to riemannian manifolds
Material type: TextSeries: Graduate texts in mathematics ; 176.Publication details: Switzerland : Springer Cham, 2018. Edition: 2nd edDescription: xiii, 437p. : 210 illustrationsISBN: 9783030801069Subject(s): Differential geometry | Riemannian geometry | Riemannian metrics | Riemannian submanifolds | Gauss-Bonnet theorem | Jacobi fields | Curvature and topology | Geodesics | Levi-Cevita connectionDDC classification: 514.7 Online resources: Table of Contents | Reviews Summary: This textbook is designed for a one or two semester graduate course on Riemannian geometry for students who are familiar with topological and differentiable manifolds. The second edition has been adapted, expanded, and aptly retitled from Lee’s earlier book, Riemannian Manifolds: An Introduction to Curvature. Numerous exercises and problem sets provide the student with opportunities to practice and develop skills; appendices contain a brief review of essential background material. While demonstrating the uses of most of the main technical tools needed for a careful study of Riemannian manifolds, this text focuses on ensuring that the student develops an intimate acquaintance with the geometric meaning of curvature. The reasonably broad coverage begins with a treatment of indispensable tools for working with Riemannian metrics such as connections and geodesics. Several topics have been added, including an expanded treatment of pseudo-Riemannianmetrics, a more detailed treatment of homogeneous spaces and invariant metrics, a completely revamped treatment of comparison theory based on Riccati equations, and a handful of new local-to-global theorems, to name just a few highlights.Item type | Current library | Call number | Status | Date due | Barcode |
---|---|---|---|---|---|
NBHM Books | SMS Library | 514.7 LEE-I (Browse shelf(Opens below)) | Available | N436 |
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514.7 IVE-C Cartan for beginners : differential geometry via moving frames and exterior differential systems | 514.7 KRE-D Differential geometry | 514.7 LAN-F Fundamentals of differential geometry | 514.7 LEE-I Introduction to riemannian manifolds | 514.7 MIC-T Topics in differential geometry | 514.7 NIC-L Lectures on the geometry of manifolds | 514.7 PET-R Riemannian geometry |
This textbook is designed for a one or two semester graduate course on Riemannian geometry for students who are familiar with topological and differentiable manifolds. The second edition has been adapted, expanded, and aptly retitled from Lee’s earlier book, Riemannian Manifolds: An Introduction to Curvature. Numerous exercises and problem sets provide the student with opportunities to practice and develop skills; appendices contain a brief review of essential background material.
While demonstrating the uses of most of the main technical tools needed for a careful study of Riemannian manifolds, this text focuses on ensuring that the student develops an intimate acquaintance with the geometric meaning of curvature. The reasonably broad coverage begins with a treatment of indispensable tools for working with Riemannian metrics such as connections and geodesics. Several topics have been added, including an expanded treatment of pseudo-Riemannianmetrics, a more detailed treatment of homogeneous spaces and invariant metrics, a completely revamped treatment of comparison theory based on Riccati equations, and a handful of new local-to-global theorems, to name just a few highlights.
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