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Mat. Sb., 2009, Volume 200, Number 3, Pages 75–94 (Mi msb5151)  

This article is cited in 11 scientific papers (total in 11 papers)

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

A. O. Remizov

University of Porto

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.

DOI: https://doi.org/10.4213/sm5151

Full text: PDF file (642 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2009, 200:3, 385–403

Bibliographic databases:

UDC: 517.974.8+517.922
MSC: Primary 53C50, 53C22; Secondary 34C20
Received: 01.04.2008 and 28.11.2008

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

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. O. Remizov, “Singularities of a geodesic flow on surfaces with a cuspidal edge”, Proc. Steklov Inst. Math., 268 (2010), 248–257  mathnet  crossref  mathscinet  zmath  isi  elib
    2. N. G. Pavlova, A. O. Remizov, “Geodesics on hypersurfaces in Minkowski space: singularities of signature change”, Russian Math. Surveys, 66:6 (2011), 1201–1203  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. Ghezzi R. Remizov A.O., “On a class of vector fields with discontinuities of divide-by-zero type and its applications to geodesics in singular metrics”, J. Dyn. Control Syst., 18:1 (2012), 135–158  crossref  mathscinet  zmath  isi  scopus  scopus
    4. Izumiya S., Fuster M., Ruas M., Tari F., “Differential Geometry From a Singularity Theory Viewpoint”, Differential Geometry From a Singularity Theory Viewpoint, World Scientific Publ Co Pte Ltd, 2016, 1–368  mathscinet  isi
    5. Remizov A.O., Tari F., “Singularities of the geodesic flow on surfaces with pseudo-Riemannian metrics”, Geod. Dedic., 185:1 (2016), 131–153  crossref  mathscinet  zmath  isi  scopus
    6. Khlestkov Yu.A., Sukhanova L.A., Trushkin N.S., “A geometrization of electric charge and mass by means of a solution to the Einstein and Maxwell equations for dust and a radial electric field”, Chin. J. Phys., 54:4 (2016), 614–627  crossref  mathscinet  isi  scopus
    7. Dias F.S., Tari F., “On the geometry of the cross-cap in the Minkoswki 3-space and binary differential equations”, Tohoku Math. J., 68:2 (2016), 293–328  crossref  mathscinet  zmath  isi
    8. N. G. Pavlova, A. O. Remizov, “A complete classification of generic singularities of geodesic flows on 2-surfaces with pseudo-Riemannian metrics”, Russian Math. Surveys, 72:3 (2017), 577–579  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    9. E. A. Chirkova, “Issledovanie odnoi trekhmernoi sistemy s neizolirovannymi osobymi tochkami”, Chelyab. fiz.-matem. zhurn., 3:3 (2018), 332–337  mathnet  crossref  elib
    10. N. G. Pavlova, A. O. Remizov, “Completion of the classification of generic singularities of geodesic flows in two classes of metrics”, Izv. Math., 83:1 (2019), 104–123  mathnet  crossref  crossref  adsnasa  isi  elib
    11. Ortiz-Bobadilla L. Rosales-Gonzalez E. Voronin S.M., “Analytic Classification of Foliations Induced By Germs of Holomorphic Vector Fields in (C-N,0) With Non-Isolated Singularities”, J. Dyn. Control Syst., 25:3 (2019), 491–516  crossref  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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