Search results
Results from the WOW.Com Content Network
This file contains additional information, probably added from the digital camera or scanner used to create or digitize it. If the file has been modified from its original state, some details may not fully reflect the modified file.
— Andrew Pressley: Elementary Differential Geometry, p. 183 Pressley (p. 185) explains this theorem as an expression of conservation of angular momentum about the axis of revolution when a particle moves along a geodesic under no forces other than those that keep it on the surface.
This is a list of differential geometry topics. See also glossary of differential and metric geometry and list of Lie group topics . Differential geometry of curves and surfaces
A major theorem, often called the fundamental theorem of the differential geometry of surfaces, asserts that whenever two objects satisfy the Gauss-Codazzi constraints, they will arise as the first and second fundamental forms of a regular surface. Using the first fundamental form, it is possible to define new objects on a regular surface.
Gauss's Theorema Egregium (Latin for "Remarkable Theorem") is a major result of differential geometry, proved by Carl Friedrich Gauss in 1827, that concerns the curvature of surfaces.
Tangent developable of a curve with zero torsion. The tangent developable is a developable surface; that is, it is a surface with zero Gaussian curvature.It is one of three fundamental types of developable surface; the other two are the generalized cones (the surface traced out by a one-dimensional family of lines through a fixed point), and the cylinders (surfaces traced out by a one ...
In the field of differential geometry in mathematics, mean curvature flow is an example of a geometric flow of hypersurfaces in a Riemannian manifold (for example, smooth surfaces in 3-dimensional Euclidean space).
In differential geometry, Fenchel's theorem is an inequality on the total absolute curvature of a closed smooth space curve, stating that it is always at least . Equivalently, the average curvature is at least 2 π / L {\displaystyle 2\pi /L} , where L {\displaystyle L} is the length of the curve.