English

Solving Differential Geometry

The present volume contains hints or full solutions to many of the exercises in two volumes of "Lecture Notes on Differential Geometry" by Mohammad Ghomi, Professor of Mathematics, Georgia Institute of Technology, and in the first eight chapters of the text "Riemannian Geometry" by Manfredo do Carmo, Emeritus Researcher at the IMPA. Solving problems being an essential part of the learning process, my goal is to provide those learning and teaching differential geometry with a large number of worked out exercises. Ghomi's notes and do Carmo's textbook cover most “superb” topics in “classical” differential geometry that are usually taught at the undergraduate level: the four vertex theorem, Fairy-Milnor theorem, Gauss's Theorema Egregium, and the Gauss-Bonnet theorem; and in “modern” differential geometry that are usually taught at the graduate level: geodesics, the Riemann curvature tensor, Jacobi fields, Hopf-Rinow and Hadamard theorems, and spaces of constant curvature. Therefore this solutions manual can be helpful to anyone learning or teaching differential geometry at both levels.

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