Geodesic
Shells of monotone curves
Czechoslovak Mathematical Journal, Tome 65 (2015) no. 3, pp. 677-699.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We determine in $\mathbb {R}^n$ the form of curves $C$ corresponding to strictly monotone functions as well as the components of affine connections $\nabla $ for which any image of $C$ under a compact-free group $\Omega $ of affinities containing the translation group is a geodesic with respect to $\nabla $. Special attention is paid to the case that $\Omega $ contains many dilatations or that $C$ is a curve in $\mathbb {R}^3$. If $C$ is a curve in $\mathbb {R}^3$ and $\Omega $ is the translation group then we calculate not only the components of the curvature and the Weyl tensor but we also decide when $\nabla $ yields a flat or metrizable space and compute the corresponding metric tensor.
DOI : 10.1007/s10587-015-0202-5
Classification : 51H20, 53B05, 53B20, 53B30, 53C22
Keywords: geodesic; shell of a curve; affine connection; (pseudo-)Riemannian metric; projective equivalence 
@article{10_1007_s10587_015_0202_5,
     author = {Mike\v{s}, Josef and Strambach, Karl},
     title = {Shells of monotone curves},
     journal = {Czechoslovak Mathematical Journal},
     pages = {677--699},
     publisher = {mathdoc},
     volume = {65},
     number = {3},
     year = {2015},
     doi = {10.1007/s10587-015-0202-5},
     mrnumber = {3407599},
     zbl = {06537686},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-015-0202-5/}
}
TY  - JOUR
AU  - Mikeš, Josef
AU  - Strambach, Karl
TI  - Shells of monotone curves
JO  - Czechoslovak Mathematical Journal
PY  - 2015
SP  - 677
EP  - 699
VL  - 65
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10587-015-0202-5/
DO  - 10.1007/s10587-015-0202-5
LA  - en
ID  - 10_1007_s10587_015_0202_5
ER  - 
%0 Journal Article
%A Mikeš, Josef
%A Strambach, Karl
%T Shells of monotone curves
%J Czechoslovak Mathematical Journal
%D 2015
%P 677-699
%V 65
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10587-015-0202-5/
%R 10.1007/s10587-015-0202-5
%G en
%F 10_1007_s10587_015_0202_5
Mikeš, Josef; Strambach, Karl. Shells of monotone curves. Czechoslovak Mathematical Journal, Tome 65 (2015) no. 3, pp. 677-699. doi : 10.1007/s10587-015-0202-5. http://geodesic.mathdoc.fr/articles/10.1007/s10587-015-0202-5/

Cité par Sources :