Visualization (Pics)

Here some pictures of interesting surfaces, produced with jReality

 

Darboux transforms of a homogeneous torus

 

 

Darboux transforms of a homogeneous torus which are tori of revolution  but not CMC in the 3-sphere [Le 2009]

 

 

Pseudo-Bubbleton jReality2 lobes (Darboux transform of the Clifford torus)

 

 

Compare to a Delaunay torus in the 3-sphere (torus of revolution in 3-sphere with constant mean curvature). Interesting coincidence?

 

Delaunay Torus

 

 

 

 

 

 

 

 

 

 

 

 

And a 3-lobed torus of revolution (not CMC in the 3-sphere). 

 

3-lobes (Darboux transform of the Clifford torus)

3 lobes (Darboux transform of the Clifford torus), v2

 

 

More lobes.....

 

 

4 lobes (Darboux transform of Clifford torus)

 

5 lobes (Darboux transform of the Clifford torus)

 






CMC surfaces

 

Delaunay surface and Delaunay Bubbletons

 

DelaunayDelaunay Bubbleton   Two step Bubbleton

 

 

 

 

Wente tori

 

 

Wente 43

Wente 43 open


Wente 65












Minimal surfaces

Helicoid and Catenoid

 

 

Helicoid

Catenoid



Willmore tori

Willmore cylinder and Willmore tori, all  obtained by a Darboux transform of a (covering of) the Clifford torus, [G-L 2009].

 

 

willmore cylinder clifford n-fold 1

 

 

clifford n-fold 2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Hamiltonian Stationary Lagrangian tori

 

Castro Urbano tori [L-R 2008]

 

 

Castro Urbano 1Castro Urbano 2 

 

 

 

 

 

 

 

 

 

 

 

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