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2004 | 2 | 4 | 516-526
Tytuł artykułu

Distinguished geodesics and jacobi fields on first order jet spaces

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In the framework of jet spaces endowed with a non-linear connection, the special curves of these spaces (h-paths, v-paths, stationary curves and geodesics) which extend the corresponding notions from Riemannian geometry are characterized. The main geometric objects and the paths are described and, in the case when the vertical metric is independent of fiber coordinates, the first two variations of energy and the extended Jacobi field equations are derived.
Wydawca
Czasopismo
Rocznik
Tom
2
Numer
4
Strony
516-526
Opis fizyczny
Daty
wydano
2004-08-01
online
2004-08-01
Bibliografia
  • [1] M. Anastasiei, I. Bucâtaru: “A notable submersion in higher order geometry”, BJGA Vol. 1, (1996), pp. 1–9.
  • [2] M. Anastasiei, I. Bucâtaru: “Jacobi fields in generalized Lagrange spaces”, Rev. Roum. Math. Pures Appl., Vol. 42, (1997), pp. 9–10, 689–695.
  • [3] V. Balan: “Lorentz-type equations in first-order jet spaces endowed with nonlinear connection” Proceedings of The First French-Romanian Colloquium of Numerical Physics, October 30–31, 2000, Bucharest, Romania, Geometry Balkan Press, (2002), pp. 105–114.
  • [4] V. Balan: “Notable curves in geometrized J 1 (T,M) jet framework”, BJGA, Vol. 8, (2003), pp. 1–10.
  • [5] V. Balan: “Synge-Beil and Riemann-Jacobi jet structures with applications to physics”, Jour. of Math. and Math. Sci, Hindawi Publ. Corp., Vol. 27, (2003), pp. 1693–1702.
  • [6] V. Balan: “Variational problems in the geometrized first-order jet framework”, Proc. Int. Workshop on Global Analysis, April 15–17, (2004), Ankara, Turkey, [to appear].
  • [7] V. Balan, N. Voicu: “Note on geodesics in distinguished jet framework”, Homagial volume in honor of Prof. K. Teleman, Univ. of Bucharest Editors, Bucharest 2004, [to appear].
  • [8] D. Bao, S.-S. Chern, Z. Shen: An Introduction to Riemann-Finsler Geometry, Springer-Verlag, 2000.
  • [9] I. Comic: “Horizontal and vertical geodesics in the Riemannian space”. Mat. Vestnik, Vol. 42, (1990), pp. 3–4, 139–153.
  • [10] B.T.M. Hassan: “Sprays ans Jacobi fields in Finsler geometry”, An. Univ. Timişoara, Ser. Şt. Mat., Vol. XIX, (1981), pp. 129–139.
  • [11] S. Kobayashi, K. Nomizu: Foundations of Differential Geometry I, II, Interscience Publishers, New York, 1963, 1969.
  • [12] J. Milnor: Morse Theory, Ann. of Math. Stud., Princeton Univ. Press, 1963.
  • [13] R. Miron: The Geometry of Lagrange Spaces: Theory and Applications, Kluwer Acad. Publishers, 1994.
  • [14] R. Miron, M. Anastasiei: The Geometry of Vector Bundles. Theory and Applications, Kluwer, Dordrecht, 1994.
  • [15] R. Miron, M. Tatoiu-Radivoiovici: “A Lagrangian theory of electromagnetism”, Rep. Math. Phys., Vol. 27, (1989), pp. 49–84. http://dx.doi.org/10.1016/0034-4877(89)90035-9
  • [16] M. Neagu: “The geometry of autonomous metrical multi-time Lagrange space of electrodynamics”, International Journal of Mathematics and Mathematical Sciences, Hindawi Publishing Corporation, (2001). http://xxx.lanl.gov/ abs/ math.DG/0010091, (2000).
  • [17] M. Neagu: “Generalized metrical multi-time Lagrangian geometry of physical fields”. http://xxx.lanl.gov/abs/math.DG/0011003, (2000).
  • [18] M. Neagu, C. Udrişte: “The geometry of metrical multi-time Lagrange spaces”, http://xxx.lanl.gov/abs/math.DG/0009071, (2000).
  • [19] D.J. Saunders: The Geometry of Jet Bundles, Cambridge University Press, 1989.
  • [20] Z. Shen: Differental Geometry of Sprays and Finsler Spaces, Kluwer Acad. Publishers, 2001.
  • [21] P.C. Stavrinos, H. Kawaguchi: “Deviation of geodesics in the gravitational field of Finslerian Space-Time”, Memoirs of Shonan Inst. of Technol., Vol. 27, (1993), pp. 35–40
  • [22] N. Voicu: “On metrical linear connections with torsion in Riemannian geometry”, An. Şt. Univ. “Al.I.Cuza”, Iaşi, [submitted].
  • [23] N. Voicu: “The Exponential Map on the Second Order Tangent Bundle”, Studia Mathematica, University of Cluj, [submitted].
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_BF02475960
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