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Differential geometry

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Differential geometry/ by Paulo Ventura Araújo.
作者:	Araújo, Paulo Ventura.
出版者:	Cham :Springer International Publishing : : 2024.,
面頁冊數:	viii, 185 p. :ill., digital ; : 24 cm.;
Contained By:	Springer Nature eBook
標題:	Differential Geometry. -
電子資源:	https://doi.org/10.1007/978-3-031-62384-4
ISBN:	9783031623844

Differential geometry
Araújo, Paulo Ventura.

Differential geometry[electronic resource] /by Paulo Ventura Araújo. - Cham :Springer International Publishing :2024. - viii, 185 p. :ill., digital ;24 cm.

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.

ISBN: 9783031623844

Standard No.: 10.1007/978-3-031-62384-4doiSubjects--Topical Terms:

671118
Differential Geometry.

LC Class. No.: QA641

Dewey Class. No.: 516.36

Differential geometry
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505 0 $a Preface -- Differentiable Curves -- Regular Surfaces -- The Geometry of the Gauss Map -- The Intrinsic Geometry of Surfaces -- The Global Geometry of Surfaces -- References -- Index.
520 $a 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.
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