Subscribe

Subscribe to our Newsletter and get informed about new publication regulary and special discounts for subscribers!

IFSL > Volume 7 > On the k-Semispray of Nonlinear Connections in...
< Back to Volume

On the k-Semispray of Nonlinear Connections in k-Tangent Bundle Geometry

Full Text PDF

Abstract:

In this paper we present a method by which is obtained a sequence of k-semisprays and two sequences of nonlinear connections on the k-tangent bundle TkM starting from a given one. Interesting particular cases appear for Lagrange and Finsler spaces of order k.

Info:

Periodical:
International Frontier Science Letters (Volume 7)
Pages:
1-10
Citation:
F. Munteanu "On the k-Semispray of Nonlinear Connections in k-Tangent Bundle Geometry", International Frontier Science Letters, Vol. 7, pp. 1-10, 2016
Online since:
March 2016
Authors:
Export:
Distribution:
References:

[1] I. Bucătaru, Horizontal Lifts in the Higher-Order Geometry, Publ. Math. Debrecen, Hungary, 56 (2000) 21-32.

[2] J. Grifone, Structure presque-tangente et connexions, I, Ann. Inst. Fourier (22) (1972) 287-334.

[3] J. Grifone, Structure presque-tangente et connexions, II, Ann. Inst. Fourier (22) (1972) 291-338.

[4] J. Grifone, M. Mehdi, On the geometry of Lagrangian mechanics with non-holonomic constraints, J. Geom. Phys. 30 (3) (1999) 187-203.

[5] M. de León, P.R. Rodrigues, Dynamical connections and non autonomous Lagrangian systems, Ann. Fac. Sci. Toulouse Math. (5) 9, 2 (1988) 171-181.

[6] R. Miron, M. Anastasiei, The Geometry of Lagrange Spaces: Theory and Applications, FTPH, 59, Kluwer Academic Publishers, (1994).

[7] R. Miron, R., The Geometry of Higher-Order Lagrange Spaces. Applications to Mechanics and Physics, FTPH, no. 82, Kluwer Academic Publishers, (1997).

[8] R. Miron, The Geometry of Higher-Order Finsler Spaces, Hadronic Press, Inc., (1998).

[9] R. Miron, D. Hrimiuc, H. Shimada, V.S. Sabău, The Geometry of Lagrange and Hamilton Spaces, FTPH, 118, Kluwer Academic Publishers, (2001).

[10] F. Munteanu, On the Semispray of Nonlinear Connections in Rheonomic Lagrange Geometry, Proc. Conf. Finsler-Lagrange Geometry, Iasi, ed. M. Anastasiei, Kluwer Academic Publishers (2003) 129-137.

[11] F. Munteanu et al, Qualitative Study of Differential Equations, Geometrical and Dynamical Aspects of Some Mechanical Systems, Numerical Treatment, and Applications, Ed. Universitaria, Craiova, 2015, pp.311-356.

[12] G. Munteanu, G. Pitiş, On the Nonlinear Connection of a Spray, Report to Math. Physics, 50 (1) (2002) 41-47.

[13] F. Munteanu, L. Popescu, The variational problem in singular rheonomic Lagrange spaces, An. Univ. Vest, Timişoara, ser. Math-Inf, 40 (1) (2002) 111-122.

[14] F. Munteanu, Second order partial differential equations (SOPDEs) and nonlinear connections on the tangent bundle of k1-velocities of a manifold, Diff. Geom. Dyn. Sys. 8 (2006) 166-180.

[15] N. Roman-Roy, M. Salgado, S. Vilarino, SOPDES and Nonlinear Connections, Publ. Math. Debrecen 78/2 (2011) 297-316.

Show More Hide