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arXiv · 2304.01839

Isoptic surfaces of segments in $S^2\times R$ and $H^2\times R$ geometries

Géza Csima
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Abstract

In this work, we examine the isoptic surface of line segments in the $S^2\times R$ and $H^2\times R$ geometries, which are from the 8 Thurston geometries. Based on the procedure first described in [10], we are able to give the isoptic surface of any segment implicitly. We rely heavily on the calculations published in [41, 42]. As a special case, we examine the Thales sphere in both geometries, which are called Thaloid. In our work we will use the projective model of $S^2\times R$ and $H^2\times R$ described by E. Moln\'ar in [20].

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Géza Csima. 2023-04-04. Isoptic surfaces of segments in $S^2\times R$ and $H^2\times R$ geometries. https://arxiv.org/abs/2304.01839

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