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Rotation indices related to Poncelet’s closure theorem

Waldemar Cieślak, Horst Martini, Witold Mozgawa (2015)

Annales UMCS, Mathematica

Let CRCr denote an annulus formed by two non-concentric circles CR, Cr in the Euclidean plane. We prove that if Poncelet’s closure theorem holds for k-gons circuminscribed to CRCr, then there exist circles inside this annulus which satisfy Poncelet’s closure theorem together with Cr, with ngons for any n > k.

Rotation surfaces with L₁-pointwise 1-type Gauss map in pseudo-Galilean space

Dae Won Yoon, Young Ho Kim, Jae Seong Jung (2015)

Annales Polonici Mathematici

We study rotation surfaces in the three-dimensional pseudo-Galilean space G₃¹ such that the Gauss map G satisfies the condition L₁G = f(G + C) for a smooth function f and a constant vector C, where L₁ is the Cheng-Yau operator.

Rotations and Hermitian Symmetric Spaces.

Lieven Vanhecke, Lorenzo Nicolodi (1990)

Monatshefte für Mathematik

Ruled surfaces treated in terms of relative geometry. (Regelflächen relativgeometrisch behandelt.)

Stamou, Georg, Magkos, Athanasios (2004)

Beiträge zur Algebra und Geometrie

Ruled Surfaces with Vanishing Second Gaussian Curvature.

D.E. Blair, Th. Koufogiorgos (1992)

Monatshefte für Mathematik

Ruled W-surfaces in Minkowski 3-space $ℜ_{1}^{3}$

Rashad A. Abdel-Baky, H. N. Abd-Ellah (2008)

Archivum Mathematicum

In this paper, we study a spacelike (timelike) ruled W-surface in Minkowski 3-space which satisfies nontrivial relation between elements of the set ${K, K_{I I}, H, H_{I I}}$ , where $(K, H)$ and $(K_{I I}, H_{I I})$ are the Gaussian and mean curvatures of the first and second fundamental forms, respectively. Finally, some examples are constructed and plotted.