On higher order geometry on anchored vector bundles

• Autorzy: Paul Popescu
• Języki publikacji: EN

Abstrakty

EN

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

Słowa kluczowe

EN

Anchored vector bundle; affine bundle; almost Lie structure; r-prolongation; r-connection; lagrangian of order r; r-semi-spray; 14R25; 44A15; 53C07; 53B15; 22A30; 70S05

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2004
• Tom: 2
• Numer: 5
• Strony: 826-839

Daty

wydano

2004-10-01

online

2004-10-01

Twórcy

autor

Paul Popescu

• University of Craiova

Bibliografia

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• [3] I. Bucataru: “Horizontal lift in the higher order geometry”, Publ. Math. Debrecen, Vol. 56(1–2), (2000), pp. 21–32.
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• [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.
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• [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.
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• [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.

Identyfikatory

DOI

10.2478/BF02475980