{"product_id":"manifolds-and-differential-geometry-9780821887134","title":"Manifolds and Differential Geometry","description":"\u003cp\u003e • Author(s): Jeffrey M Lee\u003cbr\u003e • Publisher: Orient Blackswan Pvt Ltd\u003cbr\u003e • Publisher Imprint: Orient Blackswan Pvt Ltd\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eDifferential geometry\u003c\/strong\u003e 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.\u003c\/p\u003e \u003cp\u003eThis 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.\u003c\/p\u003e \u003cp\u003eThe 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.\u003c\/p\u003e \u003cp\u003eThe book is intended for students and teachers of mathematics from high school through graduate school. It should also be of interest to working mathematicians who are curious about mathematical results in fields other than their own. It can be used by teachers at all of the above mentioned levels for the enhancement of standard curriculum materials or extra-curricular projects.\u003c\/p\u003e","brand":"Orient Blackswan Pvt Ltd","offers":[{"title":"Paperback","offer_id":45616480125079,"sku":"9780821887134","price":1397.0,"currency_code":"INR","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9780821887134.webp?v=1769294903","url":"https:\/\/atlanticbooks.com\/products\/manifolds-and-differential-geometry-9780821887134","provider":"Atlantic Books","version":"1.0","type":"link"}