The functional definition of generalized geodesics

Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F00%3A00000040" target="_blank" >RIV/47813059:19610/00:00000040 - isvavai.cz</a>
Výsledek na webu
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DOI - Digital Object Identifier
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Jazyk výsledku
angličtina
Název v původním jazyce
The functional definition of generalized geodesics
Popis výsledku v původním jazyce
In this paper, a functional definition of geodesics is introduced which allows to generalize the notion of a geodesic from smooth to topological manifolds. In the $ C^infty $ case it coincides with the classical definition of geodesics of a linear connection. If $ C^infty $-smoothness is not required, it is shown by an example that the new definition includes geodesics of non-linear, homogeneous connections. Moreover, an example of generalized geodesics which do not arise from any connection is presented. Finally, some remarks upon flatness and metrizability conditions on topological manifolds are amended.
Název v anglickém jazyce
The functional definition of generalized geodesics
Popis výsledku anglicky
In this paper, a functional definition of geodesics is introduced which allows to generalize the notion of a geodesic from smooth to topological manifolds. In the $ C^infty $ case it coincides with the classical definition of geodesics of a linear connection. If $ C^infty $-smoothness is not required, it is shown by an example that the new definition includes geodesics of non-linear, homogeneous connections. Moreover, an example of generalized geodesics which do not arise from any connection is presented. Finally, some remarks upon flatness and metrizability conditions on topological manifolds are amended.

Druh
J<sub>x</sub> - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
CEP obor
BA - Obecná matematika
OECD FORD obor
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Rok uplatnění
2000
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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