On some special surfaces connected with convex surfaces of the Lobachevskii space

V. K. Ionin

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: With a closed convex surface $\Phi$ in a Lobachevskii space we associate four special surfaces: the inscribed and circumscribed spheres, a sphere rolling freely over the inner side of $\Phi$ and an equidistant surface over whose inner side $\Phi$ rolls freely. We find an exact dependence between these four special surfaces.

Keywords: convex surface, sphere, equidistant surface.

UDC: 514.13

Received: 20.02.2002

 English version: Siberian Mathematical Journal, 2002, 43:5, 822–826

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