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Mathematics > Differential Geometry

arXiv:1401.0133 (math)
[Submitted on 31 Dec 2013 (v1), last revised 21 Jun 2014 (this version, v2)]

Title:Computing nullity and kernel vectors using NF-package: Counterexamples

Authors:Nabil L. Youssef, S. G. Elgendi
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Abstract:A computational technique for calculating nullity vectors and kernel vectors, using the new Finsler package, is introduced. As an application, three interesting counterexamples are given. The first counterexample shows that the two distributions $\mathrm{Ker}_R$ and $\N_R$ do not coincide. The second shows that the nullity distribution $\N_{P^\circ}$ is not completely integrable. The third shows that the nullity distribution $\N_\mathfrak{R}$ is not a sub-distribution of the nullity distribution $\N_{R^\circ}$.
Comments: 10 pages, LaTeX file, More references added, some typos corrected
Subjects: Differential Geometry (math.DG); General Relativity and Quantum Cosmology (gr-qc)
MSC classes: 53C60, 53B40, 58B20, 68U05, 83-08
Cite as: arXiv:1401.0133 [math.DG]
  (or arXiv:1401.0133v2 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.1401.0133
Journal reference: Comp. Phys. Commun., 185 (2014), 2859-2864
Related DOI: https://doi.org/10.1016/j.cpc.2014.07.005

Submission history

From: Nabil Youssef L [view email]
[v1] Tue, 31 Dec 2013 11:36:44 UTC (23 KB)
[v2] Sat, 21 Jun 2014 11:42:33 UTC (23 KB)
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