2009
DOI: 10.1007/s00220-009-0850-0
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Rotational Surfaces in $${\mathbb{L}^3}$$ and Solutions of the Nonlinear Sigma Model

Abstract: The Gauss map of non-degenerate surfaces in the three-dimensional Minkowski space are viewed as dynamical fields of the two-dimensional O(2, 1) Nonlinear Sigma Model. In this setting, the moduli space of solutions with rotational symmetry is completely determined. Essentially, the solutions are warped products of orbits of the 1-dimensional groups of isometries and elastic curves in either a de Sitter plane, a hyperbolic plane or an anti de Sitter plane. The main tools are the equivalence of the two-dimensiona… Show more

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Cited by 17 publications
(57 citation statements)
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References 35 publications
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“…(1) First, the surface may be considered as the graph of a function defined in each one of the coordinate planes of R 3 , indicating that the problem depends on the choice of this plane. (2) We may also assume that this plane is lightlike since the coordinate planes are not lightlike. because the domain of the integrand function is x 2 > 1 and the domain of arc tanh(x) is x 2 < 1.…”
Section: Translation Surfacesmentioning
confidence: 99%
“…(1) First, the surface may be considered as the graph of a function defined in each one of the coordinate planes of R 3 , indicating that the problem depends on the choice of this plane. (2) We may also assume that this plane is lightlike since the coordinate planes are not lightlike. because the domain of the integrand function is x 2 > 1 and the domain of arc tanh(x) is x 2 < 1.…”
Section: Translation Surfacesmentioning
confidence: 99%
“…Now, the following lemma collects some formulae that will be needed in the sequel. They can be obtained using similar computations to those included in [13,22]. For simplicity, we have eliminated the symbol in most of our notation.…”
Section: Willmore-like Energiesmentioning
confidence: 99%
“…Finally, we combine (20) and (22) to characterize the extremals of W Φ ( ) as the solutions of the following Euler-Lagrange equation:…”
Section: Lemmamentioning
confidence: 99%
See 1 more Smart Citation
“…For related literature on geometry and its applications, see, e.g., also [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26].…”
Section: XXXIImentioning
confidence: 99%