Comptes Rendus
no. 3
Differential Geometry
Critical points of the acceleration in CP2(4)
[Points critiques de l'accélération en CP2(4)]

Présenté par : Étienne Ghys

Josu Arroyo1 ; Óscar J. Garay1 ; José J. Mencía1
1 Dpto. de Matemáticas, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Aptdo 644, 48080 Bilbao, Spain
Comptes Rendus. Mathématique, Volume 345 (2007) no. 3, pp. 161-166.

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).

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).

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.06.015
Josu Arroyo 1 ; Óscar J. Garay 1 ; José J. Mencía 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 = {Josu Arroyo and \'Oscar J. Garay and Jos\'e J. Menc{\'\i}a},
     title = {Critical points of the acceleration in $ {\mathbb{CP}}^{2}(4)$},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {161--166},
     publisher = {Elsevier},
     volume = {345},
     number = {3},
     year = {2007},
     doi = {10.1016/j.crma.2007.06.015},
     language = {en},
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Josu Arroyo; Óscar J. Garay; José J. Mencía. Critical points of the acceleration in $ {\mathbb{CP}}^{2}(4)$. Comptes Rendus. Mathématique, Volume 345 (2007) no. 3, pp. 161-166. doi : 10.1016/j.crma.2007.06.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/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] M. Barros; O.J. Garay; D.A. Singer 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] M. Camarinha; F. Silva Leite; P. Crouch On the geometry of Riemannian cubic polynomials, Diferential Geom. Appl., Volume 15 (2001), pp. 107-135

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

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

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

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