02563nam a22004575i 4500 978-3-031-62384-4 DE-He213 20251030112618.0 cr nn 008mamaa 240708s2024 sz | s |||| 0|eng d 9783031623844 978-3-031-62384-4 10.1007/978-3-031-62384-4 doi QA641-670 PBMP bicssc MAT012030 bisacsh PBMP thema Araújo, Paulo Ventura. author. aut http://id.loc.gov/vocabulary/relators/aut 80187 Differential Geometry [electronic resource] / by Paulo Ventura Araújo. 1st ed. 2024. Cham : Springer International Publishing : Imprint: Springer, 2024. VIII, 185 p. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Preface -- Differentiable Curves -- Regular Surfaces -- The Geometry of the Gauss Map -- The Intrinsic Geometry of Surfaces -- The Global Geometry of Surfaces -- References -- Index. 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. Geometry, Differential. 69684 Differential Geometry. 69686 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031623837 Printed edition: 9783031623851 https://doi.org/10.1007/978-3-031-62384-4 ZDB-2-SMA ZDB-2-SXMS 61422 61422