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An Interactive Textbook on Euclidean Differential Geometry

Rolf Sulanke
Organization: Humboldt-University Berlin
Department: Mathematics
URL: http://www-irm.mathematik.hu-berlin.de/~sulanke
Revision date


The submitted zip-file contains two notebooks devoted to Euclidean curve and surface theory. These notebooks may serve as an interactive introduction into the field. The contents of the notebooks is printed in the submitted pdf-files. More information can be found at my homepage. To use the notebooks one needs five Mathematica packages, also contained in the zip-file. Three of the packages contain new Mathematica code applied and tested in the notebooks. The other two are Alfred Gray's catalogs of curves and surfaces providing many objects to be tested and investigated with the tools described in the notebooks. These five packages are intended to be a reliable basis for future developing applications of Mathematica to differential geometry.

*Education > Graduate
*Mathematics > Calculus and Analysis > Differential Geometry

arc length, tangent, binormal, principal normal, Frenet formulas, curvatures, torsion, graph, osculating circle, osculating sphere, helix, spiral, 1-parameter motion group, isogonal trajectory, absolute differential, area, asymptotic curves, Christoffel symbols, cone, conical surface, cylindrical surface, developable surface, diffeomorphism, differential, envelope, Euler's formula, evolute, exterior differential, exterior product, flat points, Frenet formulas, fundamental forms, Gauss curvature, Gauss map, geodesic, geodesic curvature, helix, hypersurface, immersion, integrability conditions, integral curvature, involute, Jacobian matrix, line congruences, loxodrome, mean curvature, Meusnier's proposition, minimal surface, moving frame, normal, normal congruence, normal curvature, orientation, osculating sphere, parallel displacement, Plücker's conoid, principal curvatures, principal curves, principal directions, regular, Riemannian curvature tensor, Riemannian manifold, Rückkehrkante, ruled surface, singular, spherical image, structure forms, submanifold, surface, surface of revolution, surface with constant Gauss curvature, tangent plane, tangent surface, tangent vector, Theorema egregium, torus, total differential, umbilic point, vector field, volume element

EuCurvesv3.pdf (1.1 MB) - PDF Document
euklsfv3.pdf (53.4 KB) - PDF Document
eudiffgeov3.zip (1.1 MB) - ZIP archive