NATURAL METRICS ON T2M AND HARMONICITY

___

  • [1] Abbassi M.T.K., Calvaruso G. and Perrone D., Harmonic sections of tangent bundles equipped with Riemannian g-natural metrics, Quarterly Journal of Mathematics - QUART J MATH , vol. 61, no. 3, 2010
  • [2] Aghasi ., Dodson C.T.J., Galanis G.N. and Suri A., Infinite dimensional second order differ- ential equations via T 2M . Nonlinear Analysis-theory Methods and Applications, vol. 67, no. 10 (2007), pp. 2829-2838.
  • [3] Antonelli P.L., and Anastasiei M., The Differential Geometry of Lagrangians which Generate Sprays, Dordrecht: Kluwer, 1996.
  • [4] Antonelli P.L., Ingarden R. S., and Matsumoto M. S., The Theory of Sprays and Finsler Spaces with Applications in Physics and Biology , Dordrecht: Kluwer, 1993.
  • [5] Boeckx E. and Vanhecke L., Harmonic and minimal vector fields on tangent and unit tangent bundles, Differential Geometry and its Applications Volume 13, Issue 1, July 2000, Pages 77-93.
  • [6] Calvaruso G., Naturally Harmonic Vector Fields, Note di Matematica, Note Mat. 1(2008), suppl. n. 1, 107-130
  • [7] Cheeger J. and Gromoll D., On the structure of complete manifolds of nonnegative curvature, Ann. of Math. 96, 413-443, (1972).
  • [8] Djaa M., Gancarzewicz J., The geometry of tangent bundles of order r, Boletin Academia , Galega de Ciencias ,Espagne, 4 (1985), 147–165
  • [9] Djaa N.E.H., Ouakkas S. , M. Djaa, Harmonic sections on the tangent bundle of order two. Annales Mathematicae et Informaticae 38( 2011) pp 15-25. 1.
  • [10] Djaa N.E.H., Boulal A. and Zagane A., Generalized warped product manifolds and Bihar- monic maps, Acta Math. Univ. Comenianae; in press, to appear (2012).
  • [11] Dodson C.T.J. and Galanis G.N., Second order tangent bundles of infinite dimensional man- ifolds, J. Geom. Phys., 52 (2004), pp. 127136.
  • [12] Eells J., Sampson J.H., Harmonic mappings of Riemannian manifolds. Amer. J. Maths. 86(1964).
  • [13] Ishihara T., Harmonic sections of tangent bundles. J. Math. Tokushima Univ. 13 (1979), 23-27.
  • [14] Konderak J.J., On Harmonic Vector Fields, Publications Matmatiques. Vol 36 (1992), 217- 288.
  • [15] Oniciuc, C., Nonlinear connections on tangent bundle and harmonicity, Ital. J. Pure Appl, 6 (1999), 109–122 .
  • [16] Opriou V., On Harmonic Maps Between Tangent Bundles. Rend.Sem.Mat, Vol 47, 1 (1989).
  • [17] Prince G., Toward a classification of dynamical symmetries in classical mechanics,Bull. Aus- tral. Math. Soc., 27 (1983) no. 1, 5371.
  • [18] Sarlet W. and Cantrijn F., Generalizations of Noethers theorem in classical mechanics, SIAM Rev., 23 (1981), no. 4, 467494.
  • [19] Saunders D.J., Jet fields, connections and second order differential equations. J. Phys.A: Math. Gen. 20, (1987) 32613270
  • [20] Yano K., Ishihara S. Tangent and Cotangent Bundles, Marcel Dekker.INC. New York 1973.