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Lectures on the Differential Geometry of Curves and Surfaces (Classic Reprint)

Lectures on the Differential Geometry of Curves and Surfaces (Classic Reprint)

Lectures on the Differential Geometry of Curves and Surfaces (Classic Reprint) by A R Forsyth

Lectures on the Differential Geometry of Curves and Surfaces (Classic Reprint)
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Author: A R Forsyth
Number of Pages: 560 pages
Published Date: 27 Sep 2015
Publisher: Forgotten Books
Publication Country: United States
Language: English
ISBN: 9781330115459
Download Link: Lectures on the Differential Geometry of Curves and Surfaces (Classic Reprint)
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Excerpt from Lectures on the Differential Geometry of Curves and Surfaces In the second section, consisting of chapters II - VI, the subject-matter is the properties of curves upon any general surface in space. Some classes of these curves (e.g. lines of curvature) are organically connected with the surface; they are completely determined by the elements of the surface to which they belong. Other curves, such as geodesics, have an equally organic relation with the surface; but they are not determined solely by the elements of the surface, for they can satisfy some arbitrarily assigned condition or conditions. Again, quite arbitrary curves and families of curves can be assumed upon a surface; not a little attention has been devoted to methods for constructing differential invariants which, being in value independent of parameters of reference, express the geometrical magnitudes of the curves, subject, of course, to the dominance of the intrinsic magnitudes of the surface containing the curve or curves. In the third section, consisting of chapters VII - XI, the subject-matter is surfaces in general, rather than particular configurations on surfaces. The most ordinary methods of point-to-point correspondence and comparison of surfaces are explained. Surfaces, which are defined (wholly or partially) by intrinsic properties, are considered, special attention being paid to minimal surfaces. Families of surfaces are discussed, according to the respective definitions that ultimately establish the families; the most obvious instance relates to those surfaces which have plane or spherical sets of lines of curvature. Lastly, a brief sketch of the simplest fundamental properties of triply orthogonal systems is given. The book concludes with a single chapter that contains an introduction to the elementary theory of congruences of curves, specially of straight lines and of circles. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

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