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Sbornik: Mathematics, 2009, Volume 200, Issue 3, Pages 385–403
DOI: https://doi.org/10.1070/SM2009v200n03ABEH004001 (Mi sm5151) 		 
This article is cited in 14 scientific papers (total in 14 papers)

Geodesics on 2-surfaces with pseudo-Riemannian metric: singularities of changes of signature

A. O. Remizov

University of Porto
English version PDF (390 kB) Citations (14)
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DOI: https://doi.org/10.1070/SM2009v200n03ABEH004001
Abstract: Smooth 2-surfaces with pseudo-Riemannian metric are considered, that is, ones with quadratic form in the tangent bundle that is not positive-definite. Degeneracy points of the form are said to be parabolic. Geodesic lines induced by this pseudo-Riemannian metric in a neighbourhood of typical parabolic points are considered, their phase portraits are obtained and extremal properties are investigated.
Bibliography: 23 titles.
Keywords: pseudo-Riemannian metric, geodesic lines, singular points, resonances, normal forms.
Received: 01.04.2008 and 28.11.2008
Russian version:
Matematicheskii Sbornik, 2009, Volume 200, Number 3, Pages 75–94
DOI: https://doi.org/10.4213/sm5151
Bibliographic databases:
UDC: 517.974.8+517.922
MSC: Primary 53C50, 53C22; Secondary 34C20
Language: English
Original paper language: Russian
Citation: A. O. Remizov, “Geodesics on 2-surfaces with pseudo-Riemannian metric: singularities of changes of signature”, Mat. Sb., 200:3 (2009), 75–94; Sb. Math., 200:3 (2009), 385–403
Citation in format AMSBIB
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    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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