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

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26110%2F10%3APU88605" target="_blank" >RIV/00216305:26110/10:PU88605 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

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

Original language description

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 theHilbert 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.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

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Continuities

Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2010

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Tavricheskiy vestnik informatiki i matematiki

ISSN

1729-3901

e-ISSN

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Volume of the periodical

2010

Issue of the periodical within the volume

1

Country of publishing house

UA - UKRAINE

Number of pages

15

Pages from-to

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UT code for WoS article

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EID of the result in the Scopus database

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