Hypersurface Constrained Elasticae in Lorentzian Space Forms

Óscar J. Garay, Álvaro Pámpano and Changhwa Woo

Advances in Mathematical Physics, 2015, vol. 2015, issue 1

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.

Date: 2015
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https://doi.org/10.1155/2015/458178

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2015:y:2015:i:1:n:458178

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