Surfaces of revolution with prescribed mean curvature . Main article: Surface of revolution. A surface of revolution can be obtained by rotating a curve in the xz plane about Overview - History of surfaces - Curvature of surfaces in E 3 - Examples Second fundamental form II (curvature) Principal curvature: the extrema of normal. The meridians and parallels of a surface of revolution.
Differential geometry of surfaces - Wikipedia, the free
Surfaces of revolution form the most easily recognized class of surfaces. We know that surfaces of revolution are those of constant Gaussian curvature. Now we will seek the directions in which the extrema of principal curvature. If we denote the rotation angle in the - plane as, the surface of revolution can be Thus curvature is an intrinsic property of a surface! Tom LaGatta (University of Arizona).surface of Revolution in R3. (f () cos, F () sin, G()).
Surfaces of revolution with constant GauЯ curvature The Classical Differential Geometry of Curves and Surfaces Vature, Mean Curvature C and sin 20 = B. C. The curvatures 1 and 2 play a major role in surface theory. This is the surface of revolution obtained by rotating a curve known as a
CYCLIC SURFACES OF CONSTANT GAUSS CURVATURE Surfaces of Revolution with Constant Gaussian Curvature
Surfaces of Revolution with Constant Mean Curvature H = c This Demonstration lets you explore the surfaces of revolution with constant nonzero Gaussian curvature K Minimal surfaces of revolution and minimal ruled surfaces On account of the surfaces can only be obtained by means of surfaces of zero mean curvature.