Differential Geometry

2024
ISBN: 978-3-031-62383-7
Verlag: Springer International Publishing

Buch, Englisch, 185 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 306 g

This textbook provides a concise introduction to the differential geometry of curves and surfaces in three-dimensional space, tailored for undergraduate students with a solid foundation in mathematical analysis and linear algebra.

The book emphasizes the geometric content of the subject, aiming to quickly cover fundamental topics such as the isoperimetric inequality and the Gauss–Bonnet theorem. This approach allows the author to extend beyond the typical content of introductory books and include additional important geometric results, such as curves and surfaces of constant width, the classification of complete surfaces of non-negative constant curvature, and Hadamard's theorem on surfaces of non-positive curvature. This range of topics offers greater variety for an introductory course.

Zielgruppe

Upper undergraduate

Autoren/Hrsg.

Araújo, Paulo Ventura

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie

Inhaltsverzeichnis

Preface.- Differentiable Curves.- Regular Surfaces.- The Geometry of the Gauss Map.- The Intrinsic Geometry of Surfaces.- The Global Geometry of Surfaces.- References.- Index.

Über Autor(innen)

Paulo Ventura Araújo graduated with a degree in Mathematics from the University of Porto and obtained his doctorate from the University of Warwick. Currently, he is a professor at the Faculty of Sciences in Porto.