(Ebook) Differential geometry of curves and surfaces by Umehara, Masaaki; Yamada, Kotaro ISBN 9789814740234, 9789814740241, 9814740233, 9814740241

(Ebook) Differential geometry of curves and surfaces by Umehara, Masaaki; Yamada, Kotaro ISBN 9789814740234, 9789814740241, 9814740233, 9814740241

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.