Almost geodesics and special affine connection

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F20%3A73602014" target="_blank" >RIV/61989592:15310/20:73602014 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007%2Fs00025-020-01251-y" target="_blank" >https://link.springer.com/article/10.1007%2Fs00025-020-01251-y</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00025-020-01251-y" target="_blank" >10.1007/s00025-020-01251-y</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Almost geodesics and special affine connection

Popis výsledku v původním jazyce

In the present paper we continue to study almost geodesic curves and determine in Rn the form of curves C for which every image under an (n- 1 ) -dimensional algebraic torus is also an almost geodesic with respect to an affine connection ∇ with constant coefficients. We also calculate explicitly the components of ∇. For the explicit calculation of the form of curves C in the n-dimensional real space Rn that are almost geodesics with respect to an affine connection ∇ , we can suppose that with C all images of C under a real (n- 1 ) -dimensional algebraic torus are also almost geodesics. This implies that the determination of C becomes an algebraic problem. Here we use E. Beltrami’s result that a differentiable curve is a local geodesic with respect to an affine connection ∇ precisely if it is a solution of an abelian differential equation with coefficients that are functions of the components of ∇. Now we consider the special case for the connection ∇ in which every curve is almost geodesic with respect to ∇.

Název v anglickém jazyce

Almost geodesics and special affine connection

Popis výsledku anglicky

In the present paper we continue to study almost geodesic curves and determine in Rn the form of curves C for which every image under an (n- 1 ) -dimensional algebraic torus is also an almost geodesic with respect to an affine connection ∇ with constant coefficients. We also calculate explicitly the components of ∇. For the explicit calculation of the form of curves C in the n-dimensional real space Rn that are almost geodesics with respect to an affine connection ∇ , we can suppose that with C all images of C under a real (n- 1 ) -dimensional algebraic torus are also almost geodesics. This implies that the determination of C becomes an algebraic problem. Here we use E. Beltrami’s result that a differentiable curve is a local geodesic with respect to an affine connection ∇ precisely if it is a solution of an abelian differential equation with coefficients that are functions of the components of ∇. Now we consider the special case for the connection ∇ in which every curve is almost geodesic with respect to ∇.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

Results in Mathematics

ISSN

1422-6383

e-ISSN

—

Svazek periodika

75

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

8

Strana od-do

"127-1"-"127-8"

Kód UT WoS článku

000552394900002

EID výsledku v databázi Scopus

2-s2.0-85088016527