Closed geodesics on the surface of a simplexстатья
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Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
Аннотация:The closed non-self-intersecting geodesics on the surface of a three-dimensional simplex are studied. It is proved that every geodesic on an arbitrary simplex can be realized on a regular simplex. This enables us to obtain a complete classification of all geodesics and describe their structure. Conditions for the existence of geodesics are obtained for an arbitrary simplex. It is proved that a simplex has infinitely many essentially different geodesics if and only if it is isohedral. Estimates for the number of geodesics are obtained for other simplexes.