With detailed explanations and numerous examples, this textbook covers the differential geometry of surfaces in Euclidean space.
... Amer . J. Math . 62 ( 1940 ) , 243–248 . Allendoerfer , C. B. , and Weil , A. , The Gauss - Bonnet theorem for ... T. , Critical points and curvature for embedded polyhedra , J. Diff . Geom . 1 ( 1967 ) , 245–256 . " Critical points and ...
The text contains many problems and solutions, permitting the reader to apply the theorems and to see concrete developments of the abstract theory.
This English edition could serve as a text for a first year graduate course on differential geometry, as did for a long time the Chicago Notes of Chern mentioned in the Preface to the German Edition.
... ( u2 + $ 2 ) dv2 Let the surface of revolution isometric with ( 1 ) be r = ( g ( u ) cos v , g ( u ) sin v , f ( u ) ) As in Example 3 of 2.14 , the metric of the surface of revolution is ds22 = ( 812 + fi2 ) du2 + g2 dv2 Since ds2 = ds2 ...
The text contains many problems and solutions, permitting the reader to apply the theorems and to see concrete developments of the abstract theory.
This book, unlike other introductory texts in differential geometry, develops the architecture necessary to introduce symplectic and contact geometry alongside its Riemannian cousin.
Differential Geometry - A First Course
A first course in differential geometry is assumed; the authors’ companion volume Differential Geometry and Lie Groups: A Computational Perspective provides the ideal preparation.
It is a subject that contains some of the most beautiful and profound results in mathematics yet many of these are accessible to higher-level undergraduates.
This book is based on the full year Ph.D. qualifying course on differentiable manifolds, global calculus, differential geometry, and related topics, given by the author at Washington University several times over a twenty year period.