This book provides an introduction to the basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas. This new edition includes new chapters, sections, examples, and exercises. From the reviews: "There are many books on the fundamentals of differential geometry, but this one is quite exceptional; this is not surprising for those who know Serge Lang's books." --EMS NEWSLETTER
This is the third version of a book on differential manifolds.
Topics in Differential Geometry
This two-volume introduction to differential geometry, part of Wiley's popular Classics Library, lays the foundation for understanding an area of study that has become vital to contemporary mathematics.
This volume is the prerequisite to the analytic and geometric study of nonlinear systems.
This book provides an introduction to topology, differential topology, and differential geometry.
A famous Swiss professor gave a student’s course in Basel on Riemann surfaces.
This text employs vector methods to explore the classical theory of curves and surfaces. Topics include basic theory of tensor algebra, tensor calculus, calculus of differential forms, and elements of Riemannian geometry. 1959 edition.
... C-valued function on the set Ok O Ok, given by pore C–(0}. The transition function writes (ps, ..., p. 1) as the function of (p1, ..., p.m_1) given as follows: If i < ko then p = p/pp. If k < i < k, then p = p, 11/pio. p = 1/pio.
This book presents, in a concise and direct manner, the appropriate mathematical formalism and fundamentals of differential topology and differential geometry, together with essential applications in many branches of physics.
Assuming only a knowledge of basic calculus, this text's elementary development of tensor theory focuses on concepts related to vector analysis. The book also forms an introduction to metric differential geometry. 1962 edition.