Differential Geometry. Space curves, fundamental quadratic forms,
geodesics; geodesic curvature, parallels, coordinates, torsion;
isometric mapping; Gauss-Weingarten, Gauss-Codazzi equations;
Christoffel symbols, Dupin indicatrix, asymptotic directions and
lines.

SolitaryRoad.com

Website owner: James Miller

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# Differential Geometry

Select from the following:
Curves in the plane, derivative of arc length, curvature, radius of curvature, circle of curvature, evolute

Space curves, tangent vector, principal normal, binormal, curvature, torsion, Frenet-Serret formulas

Lines and planes in space

Vector functions of a vector variable, directional derivatives

Surfaces, surface representation, simple surface
elements, curvilinear coordinates, surface normals, surface curves,
first and second fundamental quadratic forms, osculating paraboloid,
surface area

Surface curvature: normal, total and mean curvature, Euler's theorem, Meusnier's theorem, umbilical point, Rodrigues' Formula, lines of curvature

Curvature of a curve on a surface

Dupin indicatrix, asymptotic directions and lines

Christoffel symbols of the first and second kind

Gauss-Weingarten equations, Gauss-Codazzi equations, Fundamental Theorem of Surfaces

Geodesics, geodesic curvature, geodesic parallels,
geodesic coordinates, geodesic torsion, Gauss-Bonnet theorem

Surface maps, conformal maps, isothermic surfaces,
area-preserving maps

Isometric mapping, intrinsic property

Envelopes, characteristics, tangent surface of a space curve, ruled surfaces, developable surfaces

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