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LAMÉ SURFACE





Gabriel Lamé (17951870): French engineer and
mathematician.
Other name: superellipsoid, quasiellipsoidal surface. 
Cartesian equation of : .
Cartesian parametrization: , . Volume of the associated ball: . 
The Lamé surface
is the "sphere" with radius 1 associated to the norm ;
For rational values of ,
the surface ,
part of
intersected with the eighth of a space ,
is a portion of algebraic surface written
of degree ?? ; when p is even,
and coincide.
Examples of Lamé surfaces with a = b
=
c:
octahedral surface  plane  
sphere:  same sphere  
quartic surface  
astroidal surface  surface of degree 18 
These surfaces can be generalized into the the ndimensional
hypersurfaces with equation
for which the volume of the associated ball is ;
the case n = 2 is of course the Lamé
curves.
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© Robert FERRÉOL 2021