Smarandache curves and their properties on null curves in lightlike cone space $\mathbb{Q}_{2}^{3}$

[2512.22204] Smarandache curves and their properties on null curves in lightlike cone space $\mathbb{Q}_{2}^{3}$ Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > General Mathematics arXiv:2512.22204 (math) [Submitted on 21 Dec 2025 ( v1 ), last revised 15 Aug 2026 (this version, v2)] Title: Smarandache curves and their properties on null curves in lightlike cone space $\mathbb{Q}_{2}^{3}$ Authors: Fatma Almaz , Bilal Tekyoldaş View a PDF of the paper titled Smarandache curves and their properties on null curves in lightlike cone space $\mathbb{Q}_{2}^{3}$, by Fatma Almaz and B\.ilal Tekyolda\c{s} View PDF HTML (experimental) Abstract: This study investigates the differential geometric properties of Smarandache curves derived from null curves defined in the ligtlike cone space $% Q_{3}^{2}\subset E_{2}^{4}$. The indefinite metric structure causes the null vectors, and hence the null curves, to have a richer geometry in this space than in Euclidean or Minkowski spaces. In this study, we analyse the kinematic properties of the null curve using the null natural Frenet frame $% \{x,\xi ,N,W\}$. We then investigate the bending, torsion, and other geometric invariants of Smarandache curves constructed as linear combinations of these frame vectors (i.e., combinations of tangent, normal, or binormal vectors). The findings reveal how the original properties of the null curve are transferred to the Smarandache curves and how the metric of this particular space affects the characteristics of the Smarandache curves. This analysis provides a new perspective on the relationships between constrained and degenerate structures in differential geometry and light-like particle dynamics in theoretical physics. Comments: 24 page, 8 figures Subjects: General Mathematics (math.GM) MSC classes: 53B30, 53C50, 14H45 Cite as: arXiv:2512.22204 [math.GM] (or arXiv:2512.22204v2 [math.GM] for this version) https://doi.org/10.48550/arXiv.2512.22204 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Fatma Almaz [ view email ] [v1] Sun, 21 Dec 2025 14:28:25 UTC (15 KB) [v2] Sat, 15 Aug 2026 11:24:46 UTC (1,286 KB) Full-text links: Access Paper: View a PDF of the paper titled Smarandache curves and their properties on null curves in lightlike cone space $\mathbb{Q}_{2}^{3}$, by Fatma Almaz and B\.ilal Tekyolda\c{s} View PDF HTML (experimental) TeX Source view license Current browse context: math.GM < prev | next > new | recent | 2025-12 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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