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.
Citation:
A. O. Remizov, “Geodesics on 2-surfaces with pseudo-Riemannian metric: singularities of changes of signature”, Sb. Math., 200:3 (2009), 385–403
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\paper Geodesics on 2-surfaces with pseudo-Riemannian metric: singularities of changes of signature
\jour Sb. Math.
\yr 2009
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\pages 385--403
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Linking options:
https://www.mathnet.ru/eng/sm5151
https://doi.org/10.1070/SM2009v200n03ABEH004001
https://www.mathnet.ru/eng/sm/v200/i3/p75
This publication is cited in the following 14 articles:
A. O. Remizov, “Singulyarnosti kvazilineinykh differentsialnykh uravnenii”, Dalnevost. matem. zhurn., 23:1 (2023), 85–105
Honda A., Saji K., Teramoto K., “Mixed Type Surfaces With Bounded Gaussian Curvature in Three-Dimensional Lorentzian Manifolds”, Adv. Math., 365 (2020), 107036
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
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
E. A. Chirkova, “Issledovanie odnoi trekhmernoi sistemy s neizolirovannymi osobymi tochkami”, Chelyab. fiz.-matem. zhurn., 3:3 (2018), 332–337
N. G. Pavlova, A. O. Remizov, Springer Proceedings in Mathematics & Statistics, 222, Singularities and Foliations. Geometry, Topology and Applications, 2018, 135
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
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
Remizov A.O., Tari F., “Singularities of the geodesic flow on surfaces with pseudo-Riemannian metrics”, Geod. Dedic., 185:1 (2016), 131–153
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
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
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
N. G. Pavlova, A. O. Remizov, “Geodesics on hypersurfaces in Minkowski space: singularities of signature change”, Russian Math. Surveys, 66:6 (2011), 1201–1203
A. O. Remizov, “Singularities of a geodesic flow on surfaces with a cuspidal edge”, Proc. Steklov Inst. Math., 268 (2010), 248–257
Citation in format AMSBIB
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