Detail publikace

Straight Lines in Three-Dimensional Space and the Ultrahyperbolic Equation.

CHRASTINOVÁ, V.

Originální název

Straight Lines in Three-Dimensional Space and the Ultrahyperbolic Equation.

Typ

článek v časopise - ostatní, Jost

Jazyk

angličtina

Originální abstrakt

The straight lines in three-dimensional vector space realize the shortest distance for various metrics. This property is reformulated in terms of the inverse problem of the calculus of variations and closely related to the ultrahyperbolic equation with four independent variables. The interrelation is useful in both directions. For instance, polynomial solutions of the ultrahyperbolic equation provide all polynomial metrics with extremals the straight lines and conversely, a~slight generalization of the Hilbert metrics leads to rather nontrivial (multi-valued or focusing) solutions of the ultrahyperbolic equation. In general, the article clarifies some well-known achievements concerning the 4th Hilbert Problem.

Klíčová slova

Inverse problem of the calculus of variations, Poincar\'{e}-Cartan form, ultrahyperbolic equation, Hilbert projective metrics, 4th Hilbert Problem.

Autoři

CHRASTINOVÁ, V.

Rok RIV

2010

Vydáno

31. 7. 2010

Nakladatel

Krymské vědecké centrum národní akademie věd

Místo

Kiev

ISSN

1729-3901

Periodikum

Tavricheskiy vestnik informatiki i matematiki

Ročník

2010

Číslo

1

Stát

Ukrajina

Strany od

35

Strany do

49

Strany počet

15

BibTex

@article{BUT50311,
  author="Veronika {Chrastinová}",
  title="Straight Lines in Three-Dimensional Space and the Ultrahyperbolic Equation.",
  journal="Tavricheskiy vestnik informatiki i matematiki",
  year="2010",
  volume="2010",
  number="1",
  pages="35--49",
  issn="1729-3901"
}