Manfredo Perdigão do Carmo – Differential geometry of curves & surfaces (2018) – libgen.li

内容简介

This classic textbook provides a comprehensive introduction to the differential geometry of curves and surfaces. It begins with the local theory of curves, covering parametrized curves, arc length, curvature, and torsion. The Frenet formulas are introduced to describe the geometric properties of curves in three-dimensional space. The text then moves to the local theory of surfaces, discussing regular surfaces, the first and second fundamental forms, Gaussian and mean curvature, and the Gauss map.

The global theory of surfaces is also explored, including the Gauss-Bonnet theorem and its applications, as well as the study of geodesics and the exponential map. The author emphasizes the interplay between geometry and analysis, with numerous examples and exercises that illustrate key concepts. Written in a clear and rigorous style, this book is suitable for advanced undergraduate and graduate students in mathematics and physics.

The 2018 edition, published by Dover Publications, is a reprint of the original work, making this foundational text accessible to a new generation of readers.

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