Artículo
Henry, G. "A new formalism for the study of natural tensor fields of type (0, 2) on manifolds and fibrations" (2011) JP Journal of Geometry and Topology. 11(2):147-180
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Abstract:
In order to study tensor fields of type (0, 2) on manifolds and fibrations we introduce a new formalism that we called s-space. The s-spaces induced a one to one correspondence between the (0, 2) tensor fields and some differential matricial applications. Using this relationship, we generalized the concept of natural tensor without making use of the theory of natural operators and differential invariants. © 2011 Pushpa Publishing House.
Registro:
| Documento: | Artículo |
| Título: | A new formalism for the study of natural tensor fields of type (0, 2) on manifolds and fibrations |
| Autor: | Henry, G. |
| Filiación: | Departamento de Matemática, FCEyN Universidad de Buenos Aires Ciudad Universitaria Pabellón I, Buenos Aires, C1428EHA, Argentina |
| Palabras clave: | Fibrations; General connections; Natural tensor fields; Riemannian manifolds |
| Año: | 2011 |
| Volumen: | 11 |
| Número: | 2 |
| Página de inicio: | 147 |
| Página de fin: | 180 |
| Título revista: | JP Journal of Geometry and Topology |
| Título revista abreviado: | JP J. Geom. Topol. |
| ISSN: | 0972415X |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0972415X_v11_n2_p147_Henry |
Referencias:
- Araujo, J., Keilhauer, G.R., Natural tensor field of type (0, 2) on the tangent and cotangent bundle of a semi-Riemannian manifold (2000) Acta Univ. Palacki. Olomuc., Fac. Rer. Nat. Mathematica, 39, pp. 7-16
- 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
- Cordero, L.A., de León, M., On the curvature of the induced Riemannian metric on the frame bundle of a Riemannian manifold (1986) J. Math. Pures Appl, 65 (9), pp. 81-91
- Dubrovin, B.A., Fomenko, A.T., Novikov, S.P., Modern Geometry, Methods and Applications. Part II, the Geometry and Topology of Manifolds (1985) Graduate Texts In Mathematics, 104, p. 430. , Springer-Verlag, New York
- Henry, G., (2009) Tensores Naturales Sobre Variedades Y Fibraciones, , http://digital.bl.fcen.uba.ar/Download/Tesis/Tesis4540Henry.pdf, Doctoral Thesis. Universidad de Buenos Aires
- Henry, G., Keilhauer, G.R., Some Relationships Between the Geometry of the Tangent Bundle and the Geometry of The Riemannian Base Manifold, , preprint
- Keilhauer, G.R., Tensor field of type (0, 2) on linear frame bundles and cotangent bundles (2000) Rend. Sem. Mat. Univ. Padova, 103, pp. 51-64
- Kolar, I., Michor, P., Slovak, J., (1993) Natural Operations In Differential Geometry, p. 434. , Springer-Verlag, Berlin
- Kowalski, O., Sekisawa, M., Natural transformation of Riemannian metrics on manifolds to metrics on tangent bundles - a classification (1988) Bull Tokyo Gakugei Univ, 4, pp. 1-29
- Kowalski, O., Sekisawa, M., Natural transformation of Riemannian metrics on manifolds to metrics on linear frame bundles - a classification (1986) Differential Geometry and Its Applications, Proceedings of the Conference, pp. 149-178. , Brno, Czechoslovakia August 24-30
- Krupka, D., Elementary theory of differential invariants, Arch (1978) Math. (Brno), 14 (4), pp. 207-214
- Krupka, D., Janyska, J., (1990) Lectures On Differential Invariants, p. 195. , Folia Facultatis Scientiarum Naturalium Universitatis Purkynianae Brunensis, Mathematica, 1, University J. E. Purkyne, Brno
- Michor, P., Gauge Theory for Fibers Bundles (1988) Extended Version of a Series of Lectures Held At the Institute of Physics of the University of Napoli
- Milnor, J., Curvatures of Lef invariant metrics on Lie groups (1976) Adv. Math, 21, pp. 293-329
- Mok, K.P., On the differential geometry of frame bundles of Riemannian manifolds (1978) J. Reine Angew. Math, 302, pp. 16-31
- O'Neill, B., The fundamental equations of a submersion (1966) Michigan Math. J, 13, pp. 459-469
Citas:
---------- APA ----------
(2011) . A new formalism for the study of natural tensor fields of type (0, 2) on manifolds and fibrations. JP Journal of Geometry and Topology, 11(2), 147-180.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0972415X_v11_n2_p147_Henry [ ]
---------- CHICAGO ----------
Henry, G. "A new formalism for the study of natural tensor fields of type (0, 2) on manifolds and fibrations" . JP Journal of Geometry and Topology 11, no. 2 (2011) : 147-180.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0972415X_v11_n2_p147_Henry [ ]
---------- MLA ----------
Henry, G. "A new formalism for the study of natural tensor fields of type (0, 2) on manifolds and fibrations" . JP Journal of Geometry and Topology, vol. 11, no. 2, 2011, pp. 147-180.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0972415X_v11_n2_p147_Henry [ ]
---------- VANCOUVER ----------
Henry, G. A new formalism for the study of natural tensor fields of type (0, 2) on manifolds and fibrations. JP J. Geom. Topol. 2011;11(2):147-180.Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0972415X_v11_n2_p147_Henry [ ]
