Flat Double Rotational Surfaces in Euclidean and Lorentz–Minkowski 4-Space

Wendy Goemans

Abstract: A new type of surfaces in 4-dimensional Euclidean and Lorentz–Minkowski space is constructed by performing two simultaneous rotations on a planar curve. In analogy with rotational surfaces, the resulting surfaces are called double rotational surfaces. Classification theorems of flat double rotational surfaces are proved. These classifications contain amongst other cones over 4-dimensional Clelia curves. As a side product these new kinds of curves in 4-space are defined.

Keywords: double rotational surface, surface of double revolution, flat surface, Clelia curve, cone over a Clelia curve

Classification (MSC2000): 53A07; 53A35

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