Differential geometry

By:

Araujo, Paulo Ventura

Material type: Text

9783031623837

Subject(s):

DDC classification:

516.36 ARA-D

Contents:

1. Differentiable Curves

2. Regular Surfaces

3. The Geometry of the Gauss Map

4. The Intrinsic Geometry of Surfaces

5. The Global Geometry of Surfaces

Summary: 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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Holdings
Item type	Current library	Collection	Call number	Status	Date due	Barcode	Item holds
Books	IIITD General Stacks	Mathematics	516.36 ARA-D (Browse shelf(Opens below))	Available		013335

Total holds: 0

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Previous	516.35 VOI-H Hodge theory and complex algebraic geometry II	516.352 MIR-A Algebraic curves and Riemann surfaces	516.352 SIL-R Rational points on elliptic curves	516.36 ARA-D Differential geometry	516.36 BAR-E Elementary differential geometry	516.36 BAR-E Elementary differential geometry	516.36 BOO-I An introduction to differentiable manifolds and Riemannian geometry	Next

Includes index

1. Differentiable Curves

2. Regular Surfaces

3. The Geometry of the Gauss Map

4. The Intrinsic Geometry of Surfaces

5. The Global Geometry of Surfaces

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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