43 citations · 163 across the 20 of their papers we have counts for
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math.AG2015
Surfaces containing two circles through each point and decomposition of quaternionic matrices
A. Pakharev, M. Skopenkov
We find all analytic surfaces in space R^3 such that through each point of the surface one can draw two circular arcs fully contained in the surface. The proof uses a new decomposi…
math.AG2011★ 8 cited
A surface containing a line and a circle through each point is a quadric
Fedor Nilov, Mikhail Skopenkov
We prove that a surface in real 3-space containing a line and a circle through each point is a quadric. We also give some particular results on the classification of surfaces conta…
math.AG2011★ 43 cited
Darboux cyclides and webs from circles
Helmut Pottmann, Ling Shi, Mikhail Skopenkov
Motivated by potential applications in architecture, we study Darboux cyclides. These algebraic surfaces of order a most 4 are a superset of Dupin cyclides and quadrics, and they c…