This 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. Readership: Undergraduate and graduate students, and researchers interested in differential geometry of curve and surface theories.

DIFFERENTIAL GEOMETRY OF CURVES AND SURFACES

Science & Math

Masaaki Umehara

Kotaro Yamada

Mathematics

World Scientific Publishing Co.

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Books by Masaaki Umehara

See the best price to sell, buy, or rent books by Masaaki Umehara. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

DIFFERENTIAL GEOMETRY OF CURVES AND SURFACES