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Hypersurface Constrained Elasticae in Lorentzian Space Forms

Author

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  • Óscar J. Garay
  • Álvaro Pámpano
  • Changhwa Woo

Abstract

We study geodesics in hypersurfaces of a Lorentzian space form M1n+1(c), which are critical curves of the M1n+1(c)‐bending energy functional, for variations constrained to lie on the hypersurface. We characterize critical geodesics showing that they live fully immersed in a totally geodesic M13(c) and that they must be of three different types. Finally, we consider the classification of surfaces in the Minkowski 3‐space foliated by critical geodesics.

Suggested Citation

  • Óscar J. Garay & Álvaro Pámpano & Changhwa Woo, 2015. "Hypersurface Constrained Elasticae in Lorentzian Space Forms," Advances in Mathematical Physics, John Wiley & Sons, vol. 2015(1).
    • Handle: RePEc:wly:jnlamp:v:2015:y:2015:i:1:n:458178
    DOI: 10.1155/2015/458178
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    References listed on IDEAS

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    1. Garay, Óscar J. & Tazawa, Yoshihiko, 2015. "Extremal curves for weighted elastic energy in surfaces of 3-space forms," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 349-362.
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