TY  - BOOK
AU  - Chow,Bennett
AU  - Chow,Yutze
TI  - Lectures on differential geometry
T2  - Graduate studies in mathematics
SN  - 9781470478049
U1  - 516.36 23
PY  - 2024///
CY  - Providence, Rhode Island
PB  - American Mathematical Society
KW  - Geometry, Differential
KW  - Riemannian geometry
KW  - Submanifolds
KW  - Geometric analysis
KW  - Ricci flow
N1  - Includes bibliographical references and index; Geometry of submanifolds of Euclidean space -- Differential calculus of submanifolds -- Tangent and tensor bundles -- Curvature and local geometry -- Smooth manifolds -- Riemannian manifolds -- Differential forms -- Gauss-Bonnet theorem -- Bundles and connections -- Elliptic and parabolic equations -- Minimal surfaces -- Geometric flows and Ricci flow
N2  - This graduate-level textbook provides a comprehensive and vertically integrated introduction to differential geometry and geometric analysis. Beginning with the classical geometry of submanifolds in Euclidean space, the book develops the foundations of smooth manifolds, Riemannian geometry, differential forms, bundles, connections, and curvature. The authors systematically introduce global geometric methods including the Gauss-Bonnet and Chern-Gauss-Bonnet theorems, comparison geometry, harmonic analysis on manifolds, and geometric topology. A substantial portion of the text is devoted to geometric analysis, including elliptic and parabolic partial differential equations, minimal surfaces, curve shortening flow, and Ricci flow on surfaces. Emphasizing both intuition and rigorous mathematical development, the book connects differential geometry with topology, analysis, and mathematical physics through numerous examples, exercises, and applications. Designed for graduate students and researchers, it serves as both a textbook and a reference work for advanced study in modern differential geometry and geometric analysis
ER  -