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Null Cartan Normal Helices in Minkowski Space-Time
Abstract
A complete theory of null Cartan normal helices in Minkowski space-time 𝔼41 is developed. Two algebraic conditions, obtained by successive differentiation of the helix invariant along a unit C-constant normal field, fully characterize null Cartan helices; the quadratic condition yields two mutually orthogonal helix axes in the Lorentzian metric. Special field types are analyzed and null Cartan cubics are shown to be normal helices. On a timelike hypersurface, a Darboux frame with six curvature functions is constructed from first principles, the normal isophotic condition is shown to reduce to a linear first-order ODE, and the existence of normal silhouettes in 𝔼41 is established.
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BibTeX
@misc{saglam2026null,
title = {{Null Cartan Normal Helices in Minkowski Space-Time}},
author = {Derya Sağlam and Umut Selvi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.01262},
eprint = {2607.01262},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.01262},
}
RIS
TY - UNPB
TI - Null Cartan Normal Helices in Minkowski Space-Time
AU - Derya Sağlam
AU - Umut Selvi
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2607.01262
UR - https://arxiv.org/abs/2607.01262
AB - A complete theory of null Cartan normal helices in Minkowski space-time 𝔼^4_1 is developed. Two algebraic conditions, obtained by successive differentiation of the helix invariant along a unit C-constant normal field, fully characterize null Cartan helices; the quadratic condition yields two mutually orthogonal helix axes in the Lorentzian metric. Special field types are analyzed and null Cartan cubics are shown to be normal helices. On a timelike hypersurface, a Darboux frame with six curvature functions is constructed from first principles, the normal isophotic condition is shown to reduce to a linear first-order ODE, and the existence of normal silhouettes in 𝔼^4_1 is established.
ER -