Author: Martín Gildardo García Alvarado
Publisher: USON
ISBN: 9789706892928
Category :
Languages : es
Pages : 190

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Book Description

Author: Sebastián Montiel
Publisher: American Mathematical Soc.
ISBN: 0821847635
Category : Mathematics
Languages : en
Pages : 395

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Book Description
Offers a focused point of view on the differential geometry of curves and surfaces. This monograph treats the Gauss - Bonnet theorem and discusses the Euler characteristic. It also covers Alexandrov's theorem on embedded compact surfaces in R3 with constant mean curvature.

Author: Ivo Terek Couto
Publisher: CRC Press
ISBN: 1000223345
Category : Mathematics
Languages : en
Pages : 351

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Book Description
Lorentz Geometry is a very important intersection between Mathematics and Physics, being the mathematical language of General Relativity. Learning this type of geometry is the first step in properly understanding questions regarding the structure of the universe, such as: What is the shape of the universe? What is a spacetime? What is the relation between gravity and curvature? Why exactly is time treated in a different manner than other spatial dimensions? Introduction to Lorentz Geometry: Curves and Surfaces intends to provide the reader with the minimum mathematical background needed to pursue these very interesting questions, by presenting the classical theory of curves and surfaces in both Euclidean and Lorentzian ambient spaces simultaneously. Features: Over 300 exercises Suitable for senior undergraduates and graduates studying Mathematics and Physics Written in an accessible style without loss of precision or mathematical rigor Solution manual available on www.routledge.com/9780367468644

Author: José Fernando Escobar
Publisher: Academia Colombiana de Ciencias Exactas Fisicas y Naturales
ISBN:
Category : Mathematics
Languages : en
Pages : 142

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Book Description

Author: Paulo Ventura Araújo
Publisher: Springer Nature
ISBN: 3031623843
Category : Electronic books
Languages : en
Pages : 190

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Book Description
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 GaussBonnet 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.

Author: José Antonio Pastor González
Publisher: Editorial CSIC - CSIC Press
ISBN: 9788400091552
Category : Mathematics
Languages : es
Pages : 388

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Book Description
La Geometría Diferencial es una disciplina presente en el núcleo central de todos los estudios de Matemáticas, así como una herramienta básica en el desarrollo de otras ciencias como Física, Biología, Arquitectura e Ingeniería. Este libro tratará de curvas y superficies, enfocado a satisfacer las necesidades de los estudiantes, tanto de grado como de máster, que requieran de esta disciplina para consolidar su formación. El texto está elaborado de forma didáctica, empleando un lenguaje directo y sencillo, con el desarrollo de demostraciones detalladas, con una relación de problemas y la resolución de éstos, y el uso del software específico. Es una buena herramienta para el aprendizaje de esta rama de las Matemáticas

Author: Hilário Alencar
Publisher: American Mathematical Society
ISBN: 1470469596
Category : Mathematics
Languages : en
Pages : 416

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Book Description
This book features plane curves—the simplest objects in differential geometry—to illustrate many deep and inspiring results in the field in an elementary and accessible way. After an introduction to the basic properties of plane curves, the authors introduce a number of complex and beautiful topics, including the rotation number (with a proof of the fundamental theorem of algebra), rotation index, Jordan curve theorem, isoperimetric inequality, convex curves, curves of constant width, and the four-vertex theorem. The last chapter connects the classical with the modern by giving an introduction to the curve-shortening flow that is based on original articles but requires a minimum of previous knowledge. Over 200 figures and more than 100 exercises illustrate the beauty of plane curves and test the reader's skills. Prerequisites are courses in standard one variable calculus and analytic geometry on the plane.

Author: Manfredo P. do Carmo
Publisher: Springer Science & Business Media
ISBN: 3642255884
Category : Mathematics
Languages : en
Pages : 492

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Book Description
This volume of selected academic papers demonstrates the significance of the contribution to mathematics made by Manfredo P. do Carmo. Twice a Guggenheim Fellow and the winner of many prestigious national and international awards, the professor at the institute of Pure and Applied Mathematics in Rio de Janeiro is well known as the author of influential textbooks such as Differential Geometry of Curves and Surfaces. The area of differential geometry is the main focus of this selection, though it also contains do Carmo's own commentaries on his life as a scientist as well as assessment of the impact of his researches and a complete list of his publications. Aspects covered in the featured papers include relations between curvature and topology, convexity and rigidity, minimal surfaces, and conformal immersions, among others. Offering more than just a retrospective focus, the volume deals with subjects of current interest to researchers, including a paper co-authored with Frank Warner on the convexity of hypersurfaces in space forms. It also presents the basic stability results for minimal surfaces in the Euclidean space obtained by the author and his collaborators. Edited by do Carmo's first student, now a celebrated academic in her own right, this collection pays tribute to one of the most distinguished mathematicians.

Author: Robert Everist Greene
Publisher: American Mathematical Soc.
ISBN: 0821814966
Category : Mathematics
Languages : en
Pages : 735

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Book Description
The third of three parts comprising Volume 54, the proceedings of the Summer Research Institute on Differential Geometry, held at the University of California, Los Angeles, July 1990 (ISBN for the set is 0-8218-1493-1). Part 3 begins with an overview by R.E. Greene of some recent trends in Riemannia

Author: Alberto Lastra
Publisher: Springer Nature
ISBN: 3030813177
Category : Mathematics
Languages : en
Pages : 293

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Book Description
This textbook provides a thorough introduction to the differential geometry of parametrized curves and surfaces, along with a wealth of applications to specific architectural elements. Geometric elements in architecture respond to practical, physical and aesthetic needs. Proper understanding of the mathematics underlying the geometry provides control over the construction. This book relates the classical mathematical theory of parametrized curves and surfaces to multiple applications in architecture. The presentation is mathematically complete with numerous figures and animations illustrating the theory, and special attention is given to some of the recent trends in the field. Solved exercises are provided to see the theory in practice. Intended as a textbook for lecture courses, Parametric Geometry of Curves and Surfaces is suitable for mathematically-inclined students in engineering, architecture and related fields, and can also serve as a textbook for traditional differential geometry courses to mathematics students. Researchers interested in the mathematics of architecture or computer-aided design will also value its combination of precise mathematics and architectural examples.