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This article is cited in 14 scientific papers (total in 14 papers)
Closed geodesics on the surface of a simplex
V. Yu. Protasov M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Abstract:
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.
Bibliography: 13 titles.
Received: 16.01.2006 and 05.07.2006
Citation:
V. Yu. Protasov, “Closed geodesics on the surface of a simplex”, Mat. Sb., 198:2 (2007), 103–120; Sb. Math., 198:2 (2007), 243–260
Linking options:
https://www.mathnet.ru/eng/sm1501https://doi.org/10.1070/SM2007v198n02ABEH003836 https://www.mathnet.ru/eng/sm/v198/i2/p103
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Abstract page: | 923 | Russian version PDF: | 476 | English version PDF: | 28 | References: | 51 | First page: | 4 |
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