Abstract
Requirements are delineated for the spacetime tangent bundle to be Kählerian. In particlar, an almost complex structure is constructed in the case of a Finsler spacetime, and its covariant derivative in terms of the bundle connection is shown to be vanishing, provided the gauge curvature field is vanishing. The Levi-Civita connection coefficients and the Riemann curvature scalar are also specified for the Kähler spacetime tangent bundle.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
H. E. Brandt, “Maximal proper acceleration and the structure of spacetime,”Found. Phys. Lett. 2, 39, 405 (1989).
H. E. Brandt, “Structure of spacetime tangent bundle,”Found. Phys. Lett. 4, 523 (1991).
H. E. Brandt, “Connections and geodesics in the spacetime tangent bundle,”Found. Phys. 21, 1285 (1991).
H. E. Brandt, “Differential geometry of spacetime tangent bundle,”Int. J. Theor. Phys. 31, 575 (1992).
H. E. Brandt, “Riemann curvature scalar of spacetime tangent bundle,”Found. Phys. Lett. 5, 43 (1992).
H. E. Brandt, “Finsler-spacetime tangent bundle,”Found. Phys. Lett. 5 (3) (1992).
K. Yano and E. T. Davies, “On the tangent bundles of Finsler and Riemannian manifolds,”Rend. Circ. Mat. Palermo 12, 211 (1963).
K. Yano and S. Ishihara,Tangent and Cotangent Bundles (Marcel Dekker, New York, 1973).
H. E. Brandt, “Differential geometry of spacetime tangent bundle,” to be published inProceedings, Second International Wigner Symposium (Goslar, Germany, 16–20 July 1991), H. D. Doebner and F. Schroeck, Jr., eds. (World Scientific, Singapore).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Brandt, H.E. Kähler spacetime tangent bundle. Found Phys Lett 5, 315–336 (1992). https://doi.org/10.1007/BF00690590
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00690590