02653nam 22005175 450 991087219140332120251217144512.09783031623844(electronic bk.)978303162383710.1007/978-3-031-62384-4(MiAaPQ)EBC31522027(Au-PeEL)EBL31522027(CKB)32704674400041(DE-He213)978-3-031-62384-4(EXLCZ)993270467440004120240708d2024 u| 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierDifferential Geometry /by Paulo Ventura Araújo1st ed. 2024.Cham :Springer International Publishing :Imprint: Springer,2024.1 online resource (190 pages)Print version: Araújo, Paulo Ventura Differential Geometry Cham : Springer International Publishing AG,c2024 9783031623837 Includes bibliographical references and index.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, DifferentialDifferential GeometryGeodèsiques (Matemàtica)thubGeometria diferencialthubLlibres electrònics.thubGeometry, Differential.Differential Geometry.Geodèsiques (Matemàtica)Geometria diferencial516.36Araújo Paulo Ventura1744153MiAaPQMiAaPQMiAaPQ9910872191403321Differential Geometry4173995UNINA