Introduction to Differential Geometry is popular PDF and ePub book, written by Joel W. Robbin in 2022-01-12, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Introduction to Differential Geometry can be Read Online from any device for your convenience.
Introduction to Differential Geometry Book PDF Summary
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.
Detail Book of Introduction to Differential Geometry PDF
- Author : Joel W. Robbin
- Release : 12 January 2022
- Publisher : Springer Nature
- ISBN : 9783662643402
- Genre : Mathematics
- Total Page : 426 pages
- Language : English
- PDF File Size : 17,8 Mb
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