首页|Congruence of degenerate surface along pseudo null curve and Landau-Lifshitz equation
Congruence of degenerate surface along pseudo null curve and Landau-Lifshitz equation
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NSTL
Elsevier
This paper is devoted to the geometry of pseudo null curve in terms of anholonomic coordinates in Minkowski space. Firstly, extended Frenet formulas for pseudo null curves are deeply discussed. Then binormal congruence of degenerate surfaces containing the s - lines and n - lines are investigated with the condition mu(b) = 0. This condition represents the necessary and sufficient condition for the existence of a one-parameter family of surfaces containing the s - lines and n - lines. Moreover, normal congruence of surfaces containing the s - lines and b - lines are examined with the condition mu(n) = 0. Again, the condition represents the necessary and sufficient condition for the existence of a one-parameter family of surfaces containing the s - lines and b - lines. Considering the compatibility conditions, Gauss-Mainardi-Codazzi equations are obtained for this binormal and congruence of surfaces, respectively. Finally, some relations are given for constructing the moving pseudo null curve with using the integrable Landau-Lifshitz equation. (C) 2022 Elsevier B.V. All rights reserved.
NSTL
Elsevier
