Finsler angle-preserving connection in dimensions N >= 3

• Autores: G. S. Asanov
• Localización: Publicationes Mathematicae Debrecen, ISSN 0033-3883, Tomus 79, Fasc. 1-2, 2011, págs. 181-210
• Idioma: inglés
• DOI: 10.5486/pmd.2011.5002
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• Resumen

  • The Finsler space is considered to be the deformated Riemannian space under the condition that the indicatrix of the Finsler space is a space of constant curvature.

    In this case, the Finslerian two-vector angle can explicitly be found, which gives rise to simple and explicit representation for the connection preserving the angle in the indicatrix-homogeneous case. The connection is metrical and the Finsler space is obtainable from the Riemannian space by means of the parallel deformation. Since also the transitivity of covariant derivative holds, in such Finsler spaces the metrical non-linear angle-preserving connection is the respective export of the metrical linear Riemannian connection. In case of the FS-space, the example can be developed which entails the explicit connection coefficients and the metric function of the Finsleroid type.