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TITEICA SURFACE


Surface studied by Titeica in 1907.
Gheorghe Titeica (1873 - 1939): Romanian mathematician.
See: http://www.emis.de/journals/BJGA/10.1/bt-sogh.pdf

 
Condition for a surface to be a Titeica surface (Monge notations): .

A Titeica surface is a surface such that the total curvature at a point M is proportional to the fourth power of the distance from the tangent plane at M to a fixed point O, called the center.

An example is the following cubic surface:

Cartesian equation: .
Cubic surface.
Total curvature: .
Distance from O to the tangent plane:  ().

See here another characteristic property of this surface.
 
 
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© Robert FERRÉOL  2017