Some geometric objects of higher order concerning extensions, semi-sprays, connections and Lagrange metrics are constructed using an anchored vector bundle.
@article{bwmeta1.element.doi-10_2478_BF02475980,
author = {Paul Popescu},
title = {On higher order geometry on anchored vector bundles},
journal = {Open Mathematics},
volume = {2},
year = {2004},
pages = {826-839},
zbl = {1114.53021},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475980}
}
Paul Popescu. On higher order geometry on anchored vector bundles. Open Mathematics, Tome 2 (2004) pp. 826-839. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475980/
[1] A. Bejancu: Vectorial Finsler connections and theory of Finsler subspaces, Seminar on Geometry and Topology, Timişoara, 1986.
[2] M.B. Boyom: Anchored vector bundles and algebroids, arXiv:math.DG/0208012.
[3] I. Bucataru: “Horizontal lift in the higher order geometry”, Publ. Math. Debrecen, Vol. 56(1–2), (2000), pp. 21–32. | Zbl 0992.53054
[4] R.L. Fernandes: “Lie algebroids, holonomy and characteristic classes”, Adv. in Math., Vol. 70, (2002), pp. 119–179 (arXiv:math-DG 0007132). http://dx.doi.org/10.1006/aima.2001.2070 | Zbl 1007.22007
[5] Frans Cantrijn and Bavo Langerock: “Generalised Connections over a Vector Bundle Map”, Diff. Geom. Appl., Vol. 18, (2003), pp. 295–317 (arXiv: math.DG/0201274). http://dx.doi.org/10.1016/S0926-2245(02)00164-X | Zbl 1036.53014
[6] R. Miron: The Geometry of Higher Order Lagrange Spaces. Applications to Mechanics and Physics, Kluwer, Dordrecht, FTPH no 82, 1997. | Zbl 0877.53001
[7] R. Miron and Gh. Atanasiu: “Compendium on the higher order Lagrange spaces”, Tensor, N.S., Vol. 53 (1993), pp. 39–57. | Zbl 0851.53012
[8] R. Miron and Gh. Atanasiu: “Differential geometry of the k-osculator bundle”, Rev. Roum. Math. Pures Appl., Vol. 41 (3–4), (1996), pp. 205–236. | Zbl 0860.53049
[9] R. Miron and M. Anastasiei: Vector bundles. Lagrange spaces. Applications to the theory of relativity, Ed. Academiei, Bucureşti, 1987. | Zbl 0616.53002
[10] R. Miron and M. Anastasiei: The Geometry of Lagrange Spaces: Theory and Applications, Kluwer Acad. Publ., 1994. | Zbl 0831.53001
[11] M. Popescu: “Connections on Finsler bundles” (The second international workshop on diff.geom. and appl. 25–28 septembrie 1995, Constanţa). An. St. Univ. Ovidius Constanţa, Seria mat., Vol. III(2), (1995), pp. 97–101.
[12] P. Popescu: “On the geometry of relative tangent spaces”, Rev. Roum. Math. Pures Appl., Vol. 37(8), (1992), pp. 727–733. | Zbl 0778.53017
[13] P. Popescu: “Almost Lie structures, derivations and R-curvature on relative tangent spaces”, Rev. Roum. Math. Pures Appl., Vol. 37(8), (1992), pp. 779–789. | Zbl 0774.53017
[14] P. Popescu: On quasi-connections on fibered manifolds, New Developements in Diff. Geom., Vol. 350, Kluwer Academic Publ., 1996, pp. 343–352. | Zbl 0899.53012
[15] P. Popescu: “Categories of modules with differentials”, Journal of Algebra, Vol. 185, (1996), pp. 50–73. http://dx.doi.org/10.1006/jabr.1996.0312
[16] M. Popescu and P. Popescu: “Geometric objects defined by almost Lie structures”, In: J.Kubarski, P. Urbanski and R. Wolak (Eds.): Lie Algebroids and Related Topics in Differential Geometry, Vol. 54, Banach Center Publ., 2001, pp. 217–233. | Zbl 1001.53011
[17] P. Popescu and M. Popescu: “A general background of higher order geometry and induced objects on subspaces”, Balkan Journal of Differential Geometry and its Applications, Vol. 7(1), (2002), pp. 79–90. | Zbl 1054.53046
[18] Y.-C. Wong: “Linear connections and quasi connections on a differentiable manifold”, Tôhoku Math J., Vol. 14, (1962), pp. 49–63. | Zbl 0114.13702