![]() There is more than enough material for a year-long course on manifolds and geometry. The first chapters of the book are suitable for a one-semester course on manifolds. There is also a section that derives the exterior calculus version of Maxwell's equations. Arnold, - Gauge Fields, Knots, and Gravity, John C. An unusual feature of the book is the inclusion of an early chapter on the differential geometry of hypersurfaces in Euclidean space. Calculus on Manifolds, Michael Spivak, - Mathematical Methods of Classical Mechanics, V.I. The book also contains material on the general theory of connections on vector bundles and an in-depth chapter on semi-Riemannian geometry that covers basic material about Riemannian manifolds and Lorentz manifolds. Differential Geometry Books Classical Differential Geometry Peter Petersen Peter Petersen Differential Geometry by Rui Loja Fernandes Rui Loja Fernandes. ![]() Included are the topics usually found in a course on differentiable manifolds, such as vector bundles, tensors, differential forms, de Rham cohomology, the Frobenius theorem and basic Lie group theory. This book is a graduate-level introduction to the tools and structures of modern differential geometry. The basic object is a smooth manifold, to which some extra structure has been attached, such as a Riemannian metric, a symplectic form, a distinguished group of symmetries, or a connection on the tangent bundle. At the same time the topic has become closely allied with developments in topology. ![]() In time, the notions of curve and surface were generalized along with associated notions such as length, volume, and curvature. Differential geometry began as the study of curves and surfaces using the methods of calculus.
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