Introduction to riemannian manifolds
Lee, John M.
Introduction to riemannian manifolds - 2nd ed. - Switzerland : Springer Cham, 2018. - xiii, 437p. : 210 illustrations - Graduate texts in mathematics, 176. 0072-5285 ; .
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.
9783030801069
Differential geometry.
Riemannian geometry
Riemannian metrics
Riemannian submanifolds
Gauss-Bonnet theorem
Jacobi fields
Curvature and topology
Geodesics
Levi-Cevita connection
514.7 / LEE-I
Introduction to riemannian manifolds - 2nd ed. - Switzerland : Springer Cham, 2018. - xiii, 437p. : 210 illustrations - Graduate texts in mathematics, 176. 0072-5285 ; .
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.
9783030801069
Differential geometry.
Riemannian geometry
Riemannian metrics
Riemannian submanifolds
Gauss-Bonnet theorem
Jacobi fields
Curvature and topology
Geodesics
Levi-Cevita connection
514.7 / LEE-I
