Complex curves as lines of geometries

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F17%3A73576292" target="_blank" >RIV/61989592:15310/17:73576292 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/content/pdf/10.1007%2Fs00025-015-0518-3.pdf" target="_blank" >https://link.springer.com/content/pdf/10.1007%2Fs00025-015-0518-3.pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00025-015-0518-3" target="_blank" >10.1007/s00025-015-0518-3</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Complex curves as lines of geometries

Popis výsledku v původním jazyce

We investigate Hjelmslev geometries (Formula presented.) having a representation in a complex affine space (Formula presented.) the lines of which are given by entire functions. If (Formula presented.) has dimension 2 and the entire functions satisfy some injectivity conditions, then (Formula presented.) is a substructure of the complex Laguerre plane. If the lines are geodesics with respect to a natural connection (Formula presented.), then a detailed classification of them as well as of the corresponding geometries is obtained. Generalizations of complex Grünwald planes play a main role in the classification. Since in the considered geometries the set of lines is invariant under the translation group of (Formula presented.), we classify all complex curves C in (Formula presented.) given by entire functions as well as the connections (Formula presented.) such that all images of C under the translation group of (Formula presented.) consist of geodesics with respect to (Formula presented.).

Název v anglickém jazyce

Complex curves as lines of geometries

Popis výsledku anglicky

We investigate Hjelmslev geometries (Formula presented.) having a representation in a complex affine space (Formula presented.) the lines of which are given by entire functions. If (Formula presented.) has dimension 2 and the entire functions satisfy some injectivity conditions, then (Formula presented.) is a substructure of the complex Laguerre plane. If the lines are geodesics with respect to a natural connection (Formula presented.), then a detailed classification of them as well as of the corresponding geometries is obtained. Generalizations of complex Grünwald planes play a main role in the classification. Since in the considered geometries the set of lines is invariant under the translation group of (Formula presented.), we classify all complex curves C in (Formula presented.) given by entire functions as well as the connections (Formula presented.) such that all images of C under the translation group of (Formula presented.) consist of geodesics with respect to (Formula presented.).

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

2017

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

71

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

22

Strana od-do

"145–165"

Kód UT WoS článku

000393692900009

EID výsledku v databázi Scopus

—