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Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds.It uses the techniques of single variable calculus, vector calculus, linear algebra and multilinear algebra.
See also multivariable calculus, list of multivariable calculus topics. Manifold. Differentiable manifold; Smooth manifold; Banach manifold; Fréchet manifold; Tensor analysis. Tangent vector
His five-volume A Comprehensive Introduction to Differential Geometry [11] is among his most influential and celebrated works. The distinctive pedagogical aim of the work, as stated in its preface, was to elucidate for graduate students the often obscure relationship between classical differential geometry—geometrically intuitive but imprecise—and its modern counterpart, replete with ...
217 Lectures on Poisson Geometry, Marius Crainic, Rui Loja Fernandes, Ioan Mărcuț (2021, ISBN 978-1-4704-6430-1) 218 Lectures on Differential Topology, Riccardo Benedetti (2021, ISBN 978-1-4704-6674-9) 219 Essentials of Tropical Combinatorics, Michael Joswig (2021, ISBN 978-1-4704-6653-4)
His "Lectures on Differential Geometry" [25] is a popular standard textbook for upper-level undergraduate courses on differential manifolds, the calculus of variations, Lie theory and the geometry of G-structures. He also published the more recent "Curvature in mathematics and physics". [26]
Notes: "Proceedings of the NATO Advanced Research Workshop and the 18th International Conference on Differential Geometric Methods in Theoretical Physics: Physics and Geometry, held July 2–8, 1988, at the University of California, Davis, Davis, California"--T.p. verso.
Transformation Groups in Differential Geometry (First ed.). Springer. ISBN 3-540-05848-6. Slovák, Jan (1993). Invariant Operators on Conformal Manifolds. Research Lecture Notes, University of Vienna (Dissertation). Sternberg, Shlomo (1983). Lectures on differential geometry. New York: Chelsea. ISBN 0-8284-0316-3.
A. Almorox, Supergauge theories in graded manifolds, in Differential Geometric Methods in Mathematical Physics, Lecture Notes in Mathematics 1251 (Springer, 1987) p. 114; D. Hernandez Ruiperez, J. Munoz Masque, Global variational calculus on graded manifolds, J. Math. Pures Appl. 63 (1984) 283