Artículo
Henry, G.; Keilhauer, G. "Some relationships between the geometry of the tangent bundle and the geometry of the riemannian base manifold" (2012) Tokyo Journal of Mathematics. 35(1):1-15
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Abstract:
We compute the curvature tensor of the tangent bundle of a Riemannian manifold endowed with a natural metric and we get some relationships between the geometry of the base manifold and the geometry of the tangent bundle.
Registro:
| Documento: | Artículo |
| Título: | Some relationships between the geometry of the tangent bundle and the geometry of the riemannian base manifold |
| Autor: | Henry, G.; Keilhauer, G. |
| Filiación: | Departamento de Matemática, FCEYN, Universidadde Buenos Aires, Ciudad Universitaria, Pabellón I, Buenos Aires C1428EHA, Argentina |
| Palabras clave: | Natural tensor fields; Riemannian manifolds; Tangent bundle |
| Año: | 2012 |
| Volumen: | 35 |
| Número: | 1 |
| Página de inicio: | 1 |
| Página de fin: | 15 |
| DOI: | http://dx.doi.org/10.3836/tjm/1342701340 |
| Título revista: | Tokyo Journal of Mathematics |
| Título revista abreviado: | Tokyo J. Math. |
| ISSN: | 03873870 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03873870_v35_n1_p1_Henry |
Referencias:
- Abbassi, M.T., Sarih, M., On some hereditary properties of riemannian G-natural metrics on tangent bundles of riemannian manifolds (2005) Differential Geom. Appl., 22 (1), pp. 19-47
- Aso, K., Notes on some properties of the sectional curvature of the tangent bundle (1981) Yokohama Math. J., 29, pp. 1-5
- Calvo, M.C., Keilhauer, G.R., Tensor field of type (0,2) on the tangent bundle of a riemannian manifold (1998) Geometriae Dedicata, 71, pp. 209-219
- Gudmundsson, S., Kappos, E., On the geometry of the tangent bundle with the cheeger-gromoll metric (2002) Tokyo J. Math., 25 (1), pp. 75-83
- Henry, G., A new formalism for the study of natural tensors of type (0,2) on manifolds and fibrations (2011) JP Journal of Geometry and Topology, 112, pp. 147-180
- Henry, G., (2009) Tensores Naturales Sobre Variedades y Fibraciones, , http://digital.bl.fcen.uba.ar/Download/Tesis/Tesis_4540_Henry.pdf, Doctoral Thesis. Universidad de Buenos Aires (In Spanish)
- Kowalski, O., Curvature of the induced riemannian metric on the tangent bundle of a riemannian manifold (1971) J. Reine Angew. Math., 250, pp. 124-129
- Kowalski, O., Sekizawa, M., Natural transformation of riemannian metrics on manifolds to metrics on tangent bundles - A classification (1988) Bull. Tokyo Gakugei. Univ., 4, pp. 1-29
- Musso, E., Tricerri, F., Riemannian metrics on the tangent bundles (1988) Ann. Mat. Pura. Appl.(4), 150, pp. 1-19
- O'Neill, B., The fundamental equations of a submersion (1966) Michigan Math. J., 13, pp. 459-469
- Sekizawa, M., Curvatures of the tangent bundles with cheeger-gromoll metric (1991) Tokyo J. Math., 14 (2), pp. 407-417
Citas:
---------- APA ----------
Henry, G. & Keilhauer, G. (2012) . Some relationships between the geometry of the tangent bundle and the geometry of the riemannian base manifold. Tokyo Journal of Mathematics, 35(1), 1-15.http://dx.doi.org/10.3836/tjm/1342701340
---------- CHICAGO ----------
Henry, G., Keilhauer, G. "Some relationships between the geometry of the tangent bundle and the geometry of the riemannian base manifold" . Tokyo Journal of Mathematics 35, no. 1 (2012) : 1-15.http://dx.doi.org/10.3836/tjm/1342701340
---------- MLA ----------
Henry, G., Keilhauer, G. "Some relationships between the geometry of the tangent bundle and the geometry of the riemannian base manifold" . Tokyo Journal of Mathematics, vol. 35, no. 1, 2012, pp. 1-15.http://dx.doi.org/10.3836/tjm/1342701340
---------- VANCOUVER ----------
Henry, G., Keilhauer, G. Some relationships between the geometry of the tangent bundle and the geometry of the riemannian base manifold. Tokyo J. Math. 2012;35(1):1-15.http://dx.doi.org/10.3836/tjm/1342701340
