Differential Geometry Of Curves And Surfaces

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Masaaki Umehara (Tokyo Inst Of Technology, Japan) Kotaro Yamada (Tokyo Inst Of Technology, Japan)

Differential Geometry Of Curves And Surfaces

Masaaki Umehara (Tokyo Inst Of Technology, Japan), Kotaro Yamada (Tokyo Inst Of Technology, Japan), Wayne Rossman (Kobe Univ, Japan) , Wayne Rossman (Kobe Univ, Japan)

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English

World Scientific Publishing Co Pte Ltd
15 May 2017

Differential & Riemannian geometry

Summary
Details

'In a class populated by students who already have some exposure to the concept of a manifold, the presence of chapter 3 in this text may make for an unusual and interesting course. The primary function of this book will be as a text for a more conventional course in the classical theory of curves and surfaces.'MAA ReviewsThis engrossing volume on curve and surface theories is the result of many years of experience the authors have had with teaching the most essential aspects of this subject. The first half of the text is suitable for a university-level course, without the need for referencing other texts, as it is completely self-contained. More advanced material in the second half of the book, including appendices, also serves more experienced students well.

Furthermore, this text is also suitable for a seminar for graduate students, and for self-study. It is written in a robust style that gives the student the opportunity to continue his study at a higher level beyond what a course would usually offer. Further material is included, for example, closed curves, enveloping curves, curves of constant width, the fundamental theorem of surface theory, constant mean curvature surfaces, and existence of curvature line coordinates.

Surface theory from the viewpoint of manifolds theory is explained, and encompasses higher level material that is useful for the more advanced student. This includes, but is not limited to, indices of umbilics, properties of cycloids, existence of conformal coordinates, and characterizing conditions for singularities.

In summary, this textbook succeeds in elucidating detailed explanations of fundamental material, where the most essential basic notions stand out clearly, but does not shy away from the more advanced topics needed for research in this field. It provides a large collection of mathematically rich supporting topics. Thus, it is an ideal first textbook in this field.

By: Masaaki Umehara (Tokyo Inst Of Technology Japan), Kotaro Yamada (Tokyo Inst Of Technology, Japan)
Translated by: Wayne Rossman (Kobe Univ Japan), Wayne Rossman (Kobe Univ, Japan)
Imprint: World Scientific Publishing Co Pte Ltd
Country of Publication: Singapore
ISBN: 9789814740234
ISBN 10: 9814740233
Pages: 328
Publication Date: 15 May 2017
Audience: College/higher education , Further / Higher Education
Format: Hardback
Publisher's Status: Active