On higher order geometry on anchored vector bundles

Paul Popescu 1
  • 1 University of Craiova

Abstract

Some geometric objects of higher order concerning extensions, semi-sprays, connections and Lagrange metrics are constructed using an anchored vector bundle.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [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.

  • [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

  • [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

  • [6] R. Miron: The Geometry of Higher Order Lagrange Spaces. Applications to Mechanics and Physics, Kluwer, Dordrecht, FTPH no 82, 1997.

  • [7] R. Miron and Gh. Atanasiu: “Compendium on the higher order Lagrange spaces”, Tensor, N.S., Vol. 53 (1993), pp. 39–57.

  • [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.

  • [9] R. Miron and M. Anastasiei: Vector bundles. Lagrange spaces. Applications to the theory of relativity, Ed. Academiei, Bucureşti, 1987.

  • [10] R. Miron and M. Anastasiei: The Geometry of Lagrange Spaces: Theory and Applications, Kluwer Acad. Publ., 1994.

  • [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.

  • [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.

  • [14] P. Popescu: On quasi-connections on fibered manifolds, New Developements in Diff. Geom., Vol. 350, Kluwer Academic Publ., 1996, pp. 343–352.

  • [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.

  • [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.

  • [18] Y.-C. Wong: “Linear connections and quasi connections on a differentiable manifold”, Tôhoku Math J., Vol. 14, (1962), pp. 49–63.

OPEN ACCESS

Journal + Issues

Open Mathematics is a fully peer-reviewed, open access, electronic journal that publishes significant and original works in all areas of mathematics. The journal publishes both research papers and comprehensive and timely survey articles. Open Math aims at presenting high-impact and relevant research on topics across the full span of mathematics.

Search