Dover Differential Geometry

Livro bastante completo quanto ao assunto dado. Também tenho o do Erwin Kreyzig mas acredito que esse seja até mais completo. A explicação do conteúdo é bastante clara e simples, sempre partindo de um exemplo fácil e evoluindo gradativamente para um mais complexo. A organização do conteúdo também facilita a compreensão, já que é dividido em capítulos que definem bem o conteúdo, como o 1 que trata da base da geometria diferencial que sera necessaria no decorrer do livro, o 2 que trata de curvatura, e assim por diante. Recomendo.

What I received is an old printing with sewn binding. the pages will not fall apart like the newer lower quality glue bound books. Just what I wanted :)

I think this must be the least expensive differential geometry book that uses Cartan's orthonormal frame method. Though more than 40 years old, the notation is essentially modern (there are a few typographical oddities which aren't really bothersome).This is a very rich book, with fascinating material on nearly every page. In fact, I think it's a bit too rich for beginners, who should probably start with a more focused text like Millman & Parker or Pressley.Table of Contents for Differential GeometryPrefaceChapter 1. Elementary Differential Geometry 1-1 Curves 1-2 Vector and Matrix Functions 1-3 Some FormulasChapter 2. Curvature 2-1 Arc Length 2-2 The Moving Frame 2-3 The Circle of CurvatureChapter 3. Evolutes and Involutes 3-1 The Riemann-Stieltjès Integral 3-2 Involutes and Evolutes 3-3 Spiral Arcs 3-4 Congruence and Homothety 3-5 The Moving PlaneChapter 4. Calculus of Variations 4-1 Euler Equations 4-2 The Isoperimetric ProblemChapter 5. Introduction to Transformation Groups 5-1 Translations and Rotations 5-2 Affine TransformationsChapter 6. Lie Group Germs 6-1 Lie Group Germs and Lie Algebras 6-2 The Adjoint Representation 6-3 One-parameter SubgroupsChapter 7. Transformation Groups 7-1 Transformation Groups 7-2 Invariants 7-3 Affine Differential GeometryChapter 8. Space Curves 8-1 Space Curves in Euclidean Geometry 8-2 Ruled Surfaces 8-3 Space Curves in Affine GeometryChapter 9. Tensors 9-1 Dual Spaces 9-2 The Tensor Product 9-3 Exterior Calculus 9-4 Manifolds and Tensor FieldsChapter 10. Surfaces 10-1 Curvatures 10-2 Examples 10-3 Integration Theory 10-4 Mappings and Deformations 10-5 Closed Surfaces 10-6 Line CongruencesChapter 11. Inner Geometry of Surfaces 11-1 Geodesics 11-2 Clifford-Klein Surfaces 11-3 The Bonnet FormulaChapter 12. Affine Geometry of Surfaces 12-1 Frenet Formulas 12-2 Special Surfaces 12-3 Curves on a SurfaceChapter 13. Riemannian Geometry 13-1 Parallelism and Curvature 13-2 Geodesics 13-3 Subspaces 13-4 Groups of Motions 13-5 Integral TheoremsChapter 14. ConnectionsAnswers to Selected ExercisesIndex

The book is fine, but it looks slightly used. The cover on it looks very worn / has quite the crease. A bit of a bummer when you purchase a new item.

A good introduction book. The reader would need a different book for recent developments in the field.