A treatise on the differential geometry of curves and surfaces
Book Description
Created especially for graduate students, this introductory treatise on differential geometry offers an unusually detailed and concrete approach. Chapter I, devoted to the theory of space curves, covers parametric equations, tangents to a curve, osculating planes, and normals. The text proceeds to examinations of the geometry of a surface in the neighborhood of a point, Gauss' method, envelopes, the moving trihedral, differential parameters, systems of curves, geodesics, conformal representation, and applications of the theory to quadrics, ruled surfaces, and other areas. The last part of the book examines the deformation of surfaces, rectilinear congruences, cyclic systems, and triply orthogonal systems of surfaces. 1909 ed.
Table Of Content
I. Curves in Space
II. Curvilinear Coordinates on a Surface. Envelopes
III. Linear Element of a Surface. Differential Parameters. Conformal Representation
IV. Geometry of a Surface in the Neighborhood of a Point
V. Fundamental Equations. The Moving Trihedral
VI. Systems of Curves. Geodesics
VII. Quadrics. Ruled Surfaces. Minimal Surfaces
VIII. Surfaces of Constant Total Curvature. W-Surfaces. Surfaces with Plane or Spherical Lines of Curvature
IX. Deformation of Surfaces
X. Deformation of Surfaces. The Method of Weingarten
XI. Infinitesimal Deformation of Surfaces
XII. Rectilinear Congruences
XIII. Cyclic Systems
XIV. Triply Orthogonal Systems of Surfaces
Index