This textbook is suitable for a one semester lecture course on differential geometry for students of mathematics or STEM disciplines with a working knowledge of analysis, linear algebra, complex analysis, and point set topology. The book treats the subject both from an extrinsic and an intrinsic view point.The first chapters give a historical overview of the field and contain an introduction to basic concepts such as manifolds and smooth maps, vector fields and flows, and Lie groups, leading up to the theorem of Frobenius. ...
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This textbook is suitable for a one semester lecture course on differential geometry for students of mathematics or STEM disciplines with a working knowledge of analysis, linear algebra, complex analysis, and point set topology. The book treats the subject both from an extrinsic and an intrinsic view point.The first chapters give a historical overview of the field and contain an introduction to basic concepts such as manifolds and smooth maps, vector fields and flows, and Lie groups, leading up to the theorem of Frobenius. Subsequent chapters deal with the Levi-Civita connection, geodesics, the Riemann curvature tensor, a proof of the Cartan-Ambrose-Hicks theorem, as well as applications to flat spaces, symmetric spaces, and constant curvature manifolds. Also included are sections about manifolds with nonpositive sectional curvature, the Ricci tensor, the scalar curvature, and the Weyl tensor. An additional chapter goes beyond the scope of a one semester lecture course and deals with subjects such as conjugate points and the Morse index, the injectivity radius, the group of isometries and the Myers-Steenrod theorem, and Donaldson's differential geometric approach to Lie algebra theory.
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Add this copy of Introduction to Differential Geometry (Springer Studium to cart. $49.83, good condition, Sold by Academic Book Solutions rated 5.0 out of 5 stars, ships from Medford, NY, UNITED STATES, published 2022 by Springer Spektrum.
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Used-Good. A copy that may have been read, minimal to no highlighting/underlining of text, no missing pages. May have a remainder mark. Spine may show signs of wear. Could be a library copy.
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New. Contains: Illustrations, color. Springer Studium Mathematik (Master) . XIII, 418 p. 45 illus. in color. Intended for professional and scholarly audience.
Add this copy of Introduction to Differential Geometry (Springer Studium to cart. $67.79, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 2022 by Springer Spektrum.
