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Super Hyperbolic Law of Cosines: same formula with different content

Geometric Topology 2022-07-26 v3 High Energy Physics - Theory Mathematical Physics math.MP

Abstract

We derive the Laws of Cosines and Sines in the super hyperbolic plane using Minkowski supergeometry and find the identical formulae to the classical case, but remarkably involving different expressions for cosines and sines of angles which include substantial fermionic corrections. In further analogy to the classical case, we apply these results to show that two parallel supergeodesics which are not ultraparallel admit a unique common orthogonal supergeodesic, and we briefly describe aspects of elementary supernumber theory, leading to a prospective analogue of the Gauss product of quadratic forms.

Keywords

Cite

@article{arxiv.2103.07709,
  title  = {Super Hyperbolic Law of Cosines: same formula with different content},
  author = {Robert Penner},
  journal= {arXiv preprint arXiv:2103.07709},
  year   = {2022}
}

Comments

24 pages. Version 2 corrects several insignificant typographical errors

R2 v1 2026-06-24T00:06:22.517Z