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 Gaussian 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. Gaussian curvature: . Distance from O to the tangent plane:  ().

See here another characteristic property of this surface.
 
 

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© Robert FERRÉOL  2017