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Sbornik: Mathematics, 2007, Volume 198, Issue 2, Pages 243–260
DOI: https://doi.org/10.1070/SM2007v198n02ABEH003836 (Mi sm1501) 		 
This article is cited in 15 scientific papers (total in 15 papers)

Closed geodesics on the surface of a simplex

V. Yu. Protasov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (281 kB) Citations (15) Russian version article
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DOI: https://doi.org/10.1070/SM2007v198n02ABEH003836
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
Bibliographic databases:
UDC: 514.113.5
MSC: Primary 51M16; Secondary 51M04, 51M20, 52B05, 53C22, 57M50
Language: English
Original paper language: Russian
Citation: V. Yu. Protasov, “Closed geodesics on the surface of a simplex”, Sb. Math., 198:2 (2007), 243–260
Citation in format AMSBIB
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\pages 243--260
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    • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математический сборник Sbornik: Mathematics
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    Abstract page:969
    Russian version PDF:486
    English version PDF:38
    References:61
    First page:4
     
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