2007/07/31 by D. H. Delphenich, David Delphenich
Earth and Planetary Sciences · Physics and Astronomy · #Citation #Computer science #High-pressure geophysics and materials #Information retrieval #Laser-Matter Interactions and Applications #Laser-Plasma Interactions and Diagnostics #Library science #Obituary #Philosophy #Theology #gr-qc
paper · pdf · doi:10.1002/andp.200610250
published as AnnalenPhys.16:615-639,1997 · 33 pages
arxiv created 2007/07/31 · openalex publication_date 2007/08/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
An alternative to the representation of complex relativity by self-dual complex 2-forms on the spacetime manifold is presented by assuming that the bundle of real 2-forms is given an almostcomplex structure. From this, one can define a complex orthogonal structure on the bundle of 2forms, which results in a more direct representation of the complex orthogonal group in three complex dimensions. The geometrical foundations of general relativity are then presented in terms of the bundle of oriented complex orthogonal 3-frames on the bundle of 2-forms in a manner that essentially parallels their construction in terms of self-dual complex 2-forms. It is shown that one can still discuss the Debever-Penrose classification of the Riemannian curvature tensor in terms of the representation presented here.