Simulation Topographical Surfaces Geographical and Geological Using Differential Geometry

Elementary Differential Geometry: Curves and Surfaces

First of all, I would like to thank my colleague Lisbeth Fajstrup for many discussion about these notes and for many of the drawings in this text. The VIDIGEO-project has provided interactive and dynamical software for illustrations of curves and associated objects which are used in the first chapters of these notes; the interactive versions are accessible at www.math.aau.dk/ ˜ raussen/VIDIGEO/...

Differential geometry of curves and surfaces

These are two books that together in a pair are intended to bring the reader through classical differential geometry of curves and surfaces into the modern differential geometry of manifolds. The first book, Differential Geometry of Curves and Surfaces, by Thomas Banchoff and Stephen Lovett, offers a complete guide for the study of classical theory of curves and surfaces and is intended as a te...

Alfred Gray Modern Differential Geometry of Curves and Surfaces

DIFFERENTIAL GEOMETRY OF CURVES AND SURFACES 2. Curves in Space

for a < t < b. The entire Section 1.3 of the notes can be immediately reformulated for curves in the space: Definition 1.3.2 (of the length of a curve over a closed interval), Definition 1.3.3 and Theorem 1.3.4 (concerning reparametrization of curves), Definition 1.3.4 (of a regular curve), Theorem 1.3.6 and Proposition 1.3.7 (concerning parametrization by arc length). As about Section 1.4 (tha...

Cubic Differentials in the Differential Geometry of Surfaces

We discuss the local differential geometry of convex affine spheres in R and of minimal Lagrangian surfaces in Hermitian symmetric spaces. In each case, there is a natural metric and cubic differential holomorphic with respect to the induced conformal structure: these data come from the Blaschke metric and Pick form for the affine spheres and from the induced metric and second fundamental form ...