Abstract
With a closed convex surface Φ in a Lobachevskii space we associate four special surfaces: the inscribed and circumscribed spheres, a sphere rolling freely over the inner side of Φ, and an equidistant surface over whose inner side Φ rolls freely. We find an exact dependence between these four special surfaces.
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References
Ionin V. K., “On some special surfaces that are connected with convex surfaces in spaces of constant curvature,” Dokl. Akad. Nauk, 379, No. 1, 22-23 (2001).
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Ionin, V.K. On Some Special Surfaces Connected with Convex Surfaces of the Lobachevskii Space. Siberian Mathematical Journal 43, 822–826 (2002). https://doi.org/10.1023/A:1020146521740
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DOI: https://doi.org/10.1023/A:1020146521740