caa a22 4500 469066067 CHVBK 20180323132909.0 cr unu---uuuuu 170328e19920401xx s 000 0 eng 10.1007/BF02726990 doi (NATIONALLICENCE)springer-10.1007/BF02726990 Space-time geometry and the bundle of biframes [Elektronische Daten] I.—Geometrical developments [K. Hammon, L. Norris] Summary: When one considers bivectors on space-time as the basic geometrical objects in place of vectors one is led to the principal bundle of biframesL 2 M in place of the linear frame bundleLM.L 2 M is thus the natural arena for studying the geometry of bivectors on space-time. In this paper we develop the geometry onL 2 M including the concepts of connections, soldering form, curvature, bitorsion, generalized Bianchi identities, and associated bundles. In particular we show that the soldering form onL 2 M is a two-form, rather than a one-form as is the soldering form onLM. The corresponding torsion of a given connection one-form onL 2 M, or bitorsion, is thus a three-form. Furthermore, we show that the structure equation for the bitorsion of a given connection onL 2 M can be recast in a form which is analogous to the field equations which occur in typical non-Abelian (Yang-Mills type) gauge theories. In this analogy, the bitorsion itself plays the role of an external geometrical source for the field equations, while conservation of the total geometrical source is guaranteed by the bitorsion Bianchi identity. Finally, we show that the introduction of a difference form onL 2 M, which is the difference between a general connection one-form onL 2 M and a connection one-form onL 2 M which is induced by a Riemannian connection one-form onLM, provides a fundamental relation between the biframe Ricci tensor and the Riemannian Einstein tensor. Società Italiana di Fisica, 1992 Unified field theories and other theories of gravitation nationallicence Global differential geometry nationallicence Fundamental problems and general formalism nationallicence Hammon K. Department of Physics, North Carolina State University, Box 8202, 27695-8202, Raleigh, NC, USA aut Norris L. Departments of Mathematics & Physics, North Carolina State University, Box 8205, 27695-8205, Raleigh, NC, USA aut Il Nuovo Cimento B (1971-1996) Società Italiana di Fisica 107/4(1992-04-01), 385-405 107:4<385 1992 107 40764 https://doi.org/10.1007/BF02726990 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02726990 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Hammon K. Department of Physics, North Carolina State University, Box 8202, 27695-8202, Raleigh, NC, USA aut NATIONALLICENCE 700 1- Norris L. Departments of Mathematics & Physics, North Carolina State University, Box 8205, 27695-8205, Raleigh, NC, USA aut NATIONALLICENCE 773 0- Il Nuovo Cimento B (1971-1996) Società Italiana di Fisica 107/4(1992-04-01), 385-405 107:4<385 1992 107 40764 Metadata rights reserved Springer special CC-BY-NC licence nationallicence SWISSBIB 469066067 BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer