![]() His publications include a book on "Matrix Algebra" and joint book with Ralph Abraham on "Transversal Mappings and Flows". ![]() In 1970 he proved a conjecture by Stephen Smale which asserts that Axiom A implies structural stability. Joel Robbin began his research in mathematical logic (and wrote a text book on this subject) and later moved on to dynamical systems and symplectic topology. Also included are sections about manifolds with nonpositive sectional curvature, the Ricci tensor, the scalar curvature, and the Weyl tensor.Īn 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. 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. 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. ![]() ![]() The book treats the subject both from an extrinsic and an intrinsic view point. 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. ![]()
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