Complex curves as lines of geometries

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Complex curves as lines of geometries
Original language description
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.).
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)