000			00000nam a2200000 a 4500
005			20251203112547.0
020			_a9780821887134
082			_a516.36 _bLEE
100			_aLee, Jeffrey M.
245			_aManifolds and differential geometry _b_
260			_aRhode Island _bAmerican Mathematical Society _c2012
300			_axiv,671 p. _c26 cm. _bPB
490			_agraduate studies in mathematics vol.107
500			_aIncludes Index
600			_b _c_
630			_ageometry, differential
630			_atopological manifolds
630			_areimannian manifolds
856			_f_
856			_a_
964			_b _c _d _e _f _g_
965			_aDifferential geometry began as the study of curves and surfaces using the methods of calculus. In time, the notions of curve and surface were generalized along with associated notions such as length, volume, and curvature. At the same time the topic has become closely allied with developments in topology. 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. This book is a graduate-level introduction to the tools and structures of modern differential geometry. 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. 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. An unusual feature of the book is the inclusion of an early chapter on the differential geometry of hypersurfaces in Euclidean space. There is also a section that derives the exterior calculus version of Maxwell's equations. The first chapters of the book are suitable for a one-semester course on manifolds. There is more than enough material for a year-long course on manifolds and geometry
997			_a203149 C 203150 C
999			_c163371 _d163371