Tensor Fields of Type (0, 2) on the Tangent Bundle of a Riemannian Manifold
To any (0, 2)-tensor field on the tangent bundle of a Riemannian manifold, we associate a global matrix function. Based on this fact, natural tensor fields are defined and characterized, essentially by means of well-known algebraic results. In the symmetric case, this classification coincides with t...
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| Formato: | Capítulo de libro |
| Lenguaje: | Inglés |
| Publicado: |
Springer Netherlands
1998
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| Acceso en línea: | Registro en Scopus DOI Handle Registro en la Biblioteca Digital |
| Aporte de: | Registro referencial: Solicitar el recurso aquí |
| Sumario: | To any (0, 2)-tensor field on the tangent bundle of a Riemannian manifold, we associate a global matrix function. Based on this fact, natural tensor fields are defined and characterized, essentially by means of well-known algebraic results. In the symmetric case, this classification coincides with the one given by Kowalski-Sekizawa; in the skew-symmetric one, it does with that obtained by Janyška. |
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| Bibliografía: | Gromoll, D., Klingenberg, W., Meyer, W., (1968) Riemannsche Geometrie im Großen, , Lecture Notes in Math. 55, Springer, New York Janyška, J., Natural 2-forms on the tangent bundle of a Riemannian manifold (1994) Rend. Cir. Mat. Palermo (2). Suppl., 32, pp. 165-174 Kolář, I., Michor, P., Slovák, J., (1993) Natural Operations in Differential Geometry, , Springer-Verlag, New York Kowalski, O., Sekizawa, M., Natural transformations of Riemannian metrics on manifolds to metrics on tangent bundles - A classification (1988) Bull. Tokyo Gakugei Univ. (4), 40, pp. 1-29 Krupka, D., Elementary theory of differential invariants (1978) Arch. Math. (Brno), 4, pp. 207-214 Krupka, D., (1979) Differential Invariants, , Lecture Notes, Faculty of Science, Purkyně University, Brno Krupka, D., Janyška, J., (1990) Lectures on Differential Invariants, , Folia Fac. Sci. Nat. Univ. Purkynianae Brunensis, Brno Krupka, D., Mikolášová, V., On the uniqueness of some differential invariants: D, [,] , ∇ (1984) Czechoslovak Math. J., 34, pp. 588-597 Musso, E., Tricerri, F., Riemannian metrics on tangent bundles (1988) Ann. Mat. Pura Appl. (4), 150, pp. 1-19 |
| ISSN: | 00465755 |
| DOI: | 10.1023/A:1005084210109 |