Journal for Geometry and Graphics 20 (2016), No. 2, 209--224
Copyright Heldermann Verlag 2016
Svetlana Ribbons with Intersecting Axes in a Hyperbolic Plane of Positive Curvature
Dept. of Geometry, Saratov State University, 410012 Astrakhanskaya 83, Saratov, Russia
In the Cayley-Klein model, a Lobachevskii plane Λ2 is realized in the projective plane P2 in the interior of an oval curve. A hyperbolic plane H of positive curvature is realized in the ideal domain of the Lobachevskii plane. We study here trajectories of the midpoint of a segment with its endpoints running along two orthogonal lines intersecting in H. Such trajectories are called Svetlana Ribbons. We prove that Cassini Ovals of the Euclidean plane can be images of Svetlana Ribbons with intersecting axes.
Keywords: Lobachevskii plane, hyperbolic plane of positive curvature, Svetlana Ribbon, Cassini Oval.
MSC: 51N25; 53A17, 51F05, 51N35, 97G50
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