Differential Geometry

This book combines classical and contemporary approaches to differential geometry, discussing properties of curves and surfaces, local and global properties of plane curves, Gaussian curvature for surfaces, and the differential geometry of Lie groups.

Format: Paperback / softback
Length: 271 pages
Publication date: 11 February 2023
Publisher: Springer Nature Switzerland AG

This comprehensive textbook seamlessly blends classical and contemporary approaches to differential geometry, providing a thorough foundation for understanding the Riemannian geometry of manifolds. Before delving into the intricate realm of manifolds, the book offers a detailed exploration of the properties of curves and surfaces, laying the groundwork for subsequent chapters. In the chapter dedicated to the differential geometry of plane curves, the reader is introduced to local and global properties of curves, their evolutes and involutes, as well as affine and projective differential geometry. The text also discusses various methods for calculating Gaussian curvature for surfaces, shedding light on their mathematical characteristics.

The curvature tensor, conjugate points, and the Laplace-Beltrami operator are meticulously examined in depth for two-dimensional surfaces, facilitating their study in the many-dimensional context. A separate chapter is devoted to the differential geometry of Lie groups, offering a comprehensive understanding of these mathematical entities and their applications.

By incorporating both classical and modern perspectives, this textbook serves as an invaluable resource for advanced students and researchers in differential geometry, mathematics, and related fields. Its comprehensive coverage, clear explanations, and extensive examples make it an essential tool for anyone seeking to deepen their knowledge in this dynamic and rapidly evolving discipline.

Weight: 438g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030922511
Edition number: 1st ed. 2022