Critical points of the acceleration in $ {\mathbb{CP}}^{2}(4)$

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

doi:10.1016/j.crma.2007.06.015

Differential Geometry

Critical points of the acceleration in

{CP}^{2} (4)

Presented by: Étienne Ghys

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

Comptes Rendus. Mathématique, Volume 345 (2007) no. 3, pp. 161-166.

Abstract
Résumé

We study the variational problem associated to the $L^{2}$ norm of the angular acceleration for curve variations of constant length. We determine the unit speed closed critical curves with constant slant in ${CP}^{2} (4)$ .

Nous étudions le problème variationnel associé à la norme $L^{2}$ 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 ${CP}^{2} (4)$ .

Received: 2007-02-02
Accepted: 2007-06-12
Published online: 2007-07-25

DOI: 10.1016/j.crma.2007.06.015

Author's affiliations:

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

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     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/

References
Cited by

[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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