Geodesic
Nonconstant Continuous Functions whose Tangential Derivative Vanishes along a Smooth Curve
Canadian mathematical bulletin, Tome 54 (2011) no. 4, pp. 706-715

Voir la notice de l'article provenant de la source Cambridge University Press

We provide a simple example showing that the tangential derivative of a continuous function $\phi $ can vanish everywhere along a curve while the variation of $\phi $ along this curve is nonzero. We give additional regularity conditions on the curve and/or the function that prevent this from happening.
DOI : 10.4153/CMB-2011-027-1
Mots-clés : 26A24, 28A15 
Moonens, Laurent. Nonconstant Continuous Functions whose Tangential Derivative Vanishes along a Smooth Curve. Canadian mathematical bulletin, Tome 54 (2011) no. 4, pp. 706-715. doi: 10.4153/CMB-2011-027-1
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