![[Image: 978-0-8176-4402-4?as=webp]](https://media.springernature.com/full/springer-static/cover-hires/book/978-0-8176-4402-4?as=webp)
Differential Geometry of Curves and Surfaces
BY Victor A. Toponogov
Summary
Victor Toponogov’s Differential Geometry of Curves and Surfaces is a concise introduction to the classical geometry of curves and surfaces, designed mainly for advanced undergraduate and beginning graduate students. The book develops the fundamental ideas of differential geometry by studying curves in Euclidean space, surface geometry, curvature, geodesics, and the distinction between intrinsic and extrinsic properties. It combines standard theoretical material with deeper results and challenging problems, allowing readers to gradually move from basic concepts toward more advanced geometric reasoning.
A major theme is understanding how local measurements, such as curvature, reveal global features of geometric objects. The text also presents important theorems related to Alexandrov’s comparison theorem, rigidity of convex surfaces, and saddle surfaces. With numerous examples, illustrations, and original exercises, the book encourages active exploration rather than passive learning. Overall, it provides a clear and rigorous pathway into differential geometry while highlighting the beauty and structure of geometric ideas.
BOOK PAGE
┌────────────────────────────────┐
│ KONSTANTINOS MICHAILIDIS │
└────────────────────────────────┘
│ KONSTANTINOS MICHAILIDIS │
└────────────────────────────────┘