2006/12/19 by Frank B. Estabrook, F. B. Estabrook, Estabrook, Frank B.
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Nonlinear Waves and Solitons #gr-qc #math.DG
paper · pdf · doi:10.48550/arxiv.gr-qc/0612113
has appeared in J. Calmet, W. M. Seiler and R. W. Tucker (Eds.), Global Integrability of Field Theories (Proceedings of GIFT 2006), 95-109, ( Karlsruhe University Press, Karlsruhe, 2006)
arxiv created 2006/12/19 · openalex publication_date 2006/12/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present two families of exterior differential systems (EDS) for non-isometric embeddings of orthonormal frame bundles over Riemannian spaces of dimension q = 2, 3, 4, 5.... into orthonormal frame bundles over flat spaces of sufficiently higher dimension. We have calculated Cartan characters showing that these EDS satisfy Cartan's test and are well-posed dynamical field theories. The first family includes a constant-coefficient (cc) EDS for classical Einstein vacuum relativity (q = 4). The second family is generated only by cc 2-forms, so these are integrable (but nonlinear) systems of partial differential equations. These calibrated field theories apparently are new, although the simplest case q = 2 turns out to embed a ruled surface of signature (1,1) in flat space of signature (2,1). Cartan forms are found to give explicit variational principles for all these dynamical theories.