2018/09/07 by D. H. Delphenich, Delphenich, D. H.
Engineering · Mathematics · Physics and Astronomy · #Advanced Materials and Mechanics #FOS: Physical sciences #Force Microscopy Techniques and Applications #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #Micro and Nano Robotics #gr-qc #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1809.02663
19 pages, 6 figures
arxiv created 2018/09/07 · openalex publication_date 2018/09/07 · arxiv updated 2018/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is shown that the geometry of parallelizable manifolds can be extended to non-parallelizable ones by extending the connection that a global frame field would define on a parallelizable manifold to a connection that a singular frame field would define on a non-parallelizable one. The resulting connection would typically have non-vanishing curvature in the neighborhood of the singular points of the frame field. The example of a 2-sphere is discussed as a motivating example and later extended to more general suspensions of parallelizable manifolds.