Differential Geometry and Topology

Accessible, concise, and self-contained, this book offers an outstanding introduction to three related subjects: differential geometry, differential topology, and dynamical systems. The authors' intuitive approach forms a treatment that is comprehensible to relative beginners, yet rigorous enough for professional mathematicians. Smooth manifolds, Riemannian metrics, affine connections, the curvature tensor, differential forms, integration on manifolds, and intersection theory provide the foundation for many applications in dynamical systems and mechanics. Topics of special interest addressed in the book include Brouwer's fixed point theorem, Morse Theory, and the geodesic flow.