Differential Structures of Frölicher Spaces on Tangent Curves

Differential-geometric structures of Frölicher spaces for a singular manifold consisting of two tangent curves are considered. Calculations for two types of structures lead either to the ∞-flatness of all curves passing from one branch to another at a singular point or to the ∞-flatness of functions...

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Veröffentlicht in:	Journal of mathematical sciences (New York, N.Y.) N.Y.), 2020-12, Vol.251 (4), p.453-461
1. Verfasser:	Burian, S. N.
Format:	Artikel
Sprache:	eng
Schlagworte:	Curves Differential geometry Flatness Mathematics Mathematics and Statistics
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description	Differential-geometric structures of Frölicher spaces for a singular manifold consisting of two tangent curves are considered. Calculations for two types of structures lead either to the ∞-flatness of all curves passing from one branch to another at a singular point or to the ∞-flatness of functions. In the second case, smooth curves can change their branch of motion, their velocity vector vanishes at the singular point.
doi_str_mv	10.1007/s10958-020-05105-4
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title	Differential Structures of Frölicher Spaces on Tangent Curves
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