no. 3
Differential Geometry
Critical points of the acceleration in CP2(4)
[Points critiques de l'accélération en CP2(4)]
Présenté par : Étienne Ghys
Arroyo, Josu1 ; Garay, Óscar J.1 ; Mencía, José J.1
1 Dpto. de Matemáticas, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Aptdo 644, 48080 Bilbao, Spain
Comptes Rendus. Mathématique, Tome 345 (2007) no. 3, pp. 161-166

We study the variational problem associated to the L2 norm of the angular acceleration for curve variations of constant length. We determine the unit speed closed critical curves with constant slant in CP2(4).

Nous étudions le problème variationnel associé à la norme L2 de l'accélération angulaire pour des variations de courbe de longueur constante. Nous déterminons les courbes critiques fermées paramétrées par des abscisses curvilignes à pente constante en CP2(4).

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.06.015

Arroyo, Josu 1 ; Garay, Óscar J. 1 ; Mencía, José J. 1

1 Dpto. de Matemáticas, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Aptdo 644, 48080 Bilbao, Spain 
@article{CRMATH_2007__345_3_161_0,
     author = {Arroyo, Josu and Garay, \'Oscar J. and Menc{\'\i}a, Jos\'e J.},
     title = {Critical points of the acceleration in $ {\mathbb{CP}}^{2}(4)$},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {161--166},
     year = {2007},
     publisher = {Elsevier},
     volume = {345},
     number = {3},
     doi = {10.1016/j.crma.2007.06.015},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.crma.2007.06.015/}
}
TY  - JOUR
AU  - Arroyo, Josu
AU  - Garay, Óscar J.
AU  - Mencía, José J.
TI  - Critical points of the acceleration in $ {\mathbb{CP}}^{2}(4)$
JO  - Comptes Rendus. Mathématique
PY  - 2007
SP  - 161
EP  - 166
VL  - 345
IS  - 3
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.1016/j.crma.2007.06.015/
DO  - 10.1016/j.crma.2007.06.015
LA  - en
ID  - CRMATH_2007__345_3_161_0
ER  - 
%0 Journal Article
%A Arroyo, Josu
%A Garay, Óscar J.
%A Mencía, José J.
%T Critical points of the acceleration in $ {\mathbb{CP}}^{2}(4)$
%J Comptes Rendus. Mathématique
%D 2007
%P 161-166
%V 345
%N 3
%I Elsevier
%U https://www.numdam.org/articles/10.1016/j.crma.2007.06.015/
%R 10.1016/j.crma.2007.06.015
%G en
%F CRMATH_2007__345_3_161_0
Arroyo, Josu; Garay, Óscar J.; Mencía, José J. Critical points of the acceleration in $ {\mathbb{CP}}^{2}(4)$. Comptes Rendus. Mathématique, Tome 345 (2007) no. 3, pp. 161-166. doi: 10.1016/j.crma.2007.06.015

[1] J. Arroyo, O.J. Garay, J.J. Mencía, Unit speed stationary points of the acceleration, Preprint

[2] Barros, M.; Garay, O.J.; Singer, D.A. Elasticae with constant slant in the complex projective plane and new examples of Willmore tori in five spheres, Tohoku Math. J., Volume 51 (1999), pp. 177-192

[3] Camarinha, M.; Silva Leite, F.; Crouch, P. On the geometry of Riemannian cubic polynomials, Diferential Geom. Appl., Volume 15 (2001), pp. 107-135

[4] Nesterenko, V.V.; Feoli, A.; Scarpetta, G. Dynamics of relativistic particle with Lagrangian dependent on acceleration, J. Math. Phys., Volume 6 (1989), pp. 465-473

[5] Noakes, L.; Heinzinger, G.; Paden, B. Cubic splines on curved spaces, IMA J. Math. Control Inform., Volume 12 (1995), pp. 399-410

[6] Noakes, L.; Popiel, T. Null Riemannian cubics in tension, IMA J. Math. Control Inform., Volume 22 (2005), pp. 477-488

Cité par Sources :