In the present work, we focused on studying the evolution of null Cartan and pseudo null curves using the Bishop frame in Minkowski space $ \mathbb{R}^{2, 1} $. We obtained the necessary and sufficient conditions for the null Cartan and pseudo null curves to be inextensible curves (the arc length is preserved). In addition, we derived the time evolution equations of the Bishop frame (TEEsBF) for these curves. Moreover, we obtained the time evolution equations of Bishop curvatures (TEEsBCs) as partial differential equations in terms of Bishop velocities. Finally, we presented some applications.
Citation: Samah Gaber, Abeer Al Elaiw. Evolution of null Cartan and pseudo null curves via the Bishop frame in Minkowski space $ \mathbb{R}^{2, 1} $[J]. AIMS Mathematics, 2025, 10(2): 3691-3709. doi: 10.3934/math.2025171
In the present work, we focused on studying the evolution of null Cartan and pseudo null curves using the Bishop frame in Minkowski space $ \mathbb{R}^{2, 1} $. We obtained the necessary and sufficient conditions for the null Cartan and pseudo null curves to be inextensible curves (the arc length is preserved). In addition, we derived the time evolution equations of the Bishop frame (TEEsBF) for these curves. Moreover, we obtained the time evolution equations of Bishop curvatures (TEEsBCs) as partial differential equations in terms of Bishop velocities. Finally, we presented some applications.
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Samah Gaber, Abeer Al Elaiw. Evolution of null Cartan and pseudo null curves via the Bishop frame in Minkowski space $ \mathbb{R}^{2, 1} $[J]. AIMS Mathematics, 2025, 10(2): 3691-3709. doi: 10.3934/math.2025171
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