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  • This contribution is concerned with metrizability of linear connections on two-manifolds and the relationship of this problem to a particular case of the so-called inverse problem of the calculus of variations. The inverse problem is not considered in its full generality, but in the following sense. Given a system of second order differential equations of a particular type when second derivatives are quadratic forms in velocities. We ask whether there are multipliers independent of time and velocities, such that the multiplied equations be variational. If this is the case then there is a lagrangian such that the corresponding extremals are described exactly by the given equations. The same problem can be reformulated in the language of metrizability of an affine connection. Three facts seem to be crutial: In dimension two, the curvature tensor can be expressed in terms of the Ricci tensor. For a nowhere flat pseudo-Riemannian two-manifold, the metric tensor is proportional to the Ricci
  • This contribution is concerned with metrizability of linear connections on two-manifolds and the relationship of this problem to a particular case of the so-called inverse problem of the calculus of variations. The inverse problem is not considered in its full generality, but in the following sense. Given a system of second order differential equations of a particular type when second derivatives are quadratic forms in velocities. We ask whether there are multipliers independent of time and velocities, such that the multiplied equations be variational. If this is the case then there is a lagrangian such that the corresponding extremals are described exactly by the given equations. The same problem can be reformulated in the language of metrizability of an affine connection. Three facts seem to be crutial: In dimension two, the curvature tensor can be expressed in terms of the Ricci tensor. For a nowhere flat pseudo-Riemannian two-manifold, the metric tensor is proportional to the Ricci (en)
  • Tento příspěvek se týká metrizovatelnosti afinní konexe na dvojdimenzionální varietě a vztahu této otázky ke speciálnímu případu tzv. inverzního problému variačního počtu. (cs)
Title
  • Linear connections on two-manifolds and SODE's
  • Linear connections on two-manifolds and SODE's (en)
  • Lineární konexe na dvojdimenzionální varietě a SODE (cs)
skos:prefLabel
  • Linear connections on two-manifolds and SODE's
  • Linear connections on two-manifolds and SODE's (en)
  • Lineární konexe na dvojdimenzionální varietě a SODE (cs)
skos:notation
  • RIV/61989592:15310/07:00004540!RIV08-MSM-15310___
http://linked.open.../vavai/riv/strany
  • 325-332
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GA201/05/2707), Z(MSM6198959214)
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 431116
http://linked.open...ai/riv/idVysledku
  • RIV/61989592:15310/07:00004540
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • Affine connection; metric tensor; geodesics; lagrangian; variational equations (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...ontrolniKodProRIV
  • [E052FAD0E699]
http://linked.open...i/riv/mistoVydani
  • Bratislava
http://linked.open...i/riv/nazevZdroje
  • Conference Proceedings APLIMAT 2007
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...iv/tvurceVysledku
  • Vanžurová, Alena
http://linked.open...n/vavai/riv/zamer
number of pages
http://purl.org/ne...btex#hasPublisher
  • Slovenská technická univerzita v Bratislave
https://schema.org/isbn
  • 978-80-969562-8-9
http://localhost/t...ganizacniJednotka
  • 15310
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