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NATURAL METRICS ON T2M AND HARMONICITY

Year 2013, Volume: 6 Issue: 1, 100 - 111, 30.04.2013

Djaa Mustapha Nour Elhouda Djaa Rafik Nasrı

Abstract


Keywords

Horizontal lift vertical lift natural metric λ-lift harmonic section

References

  • [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.

Year 2013, Volume: 6 Issue: 1, 100 - 111, 30.04.2013

Djaa Mustapha Nour Elhouda Djaa Rafik Nasrı

Abstract

References

  • [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.
There are 20 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Djaa Mustapha This is me

Nour Elhouda Djaa

Rafik Nasrı This is me

Publication Date April 30, 2013
Published in Issue Year 2013 Volume: 6 Issue: 1

Cite

APA Mustapha, D., Djaa, N. E., & Nasrı, R. (2013). NATURAL METRICS ON T2M AND HARMONICITY. International Electronic Journal of Geometry, 6(1), 100-111.
AMA Mustapha D, Djaa NE, Nasrı R. NATURAL METRICS ON T2M AND HARMONICITY. Int. Electron. J. Geom. April 2013;6(1):100-111.
Chicago Mustapha, Djaa, Nour Elhouda Djaa, and Rafik Nasrı. “NATURAL METRICS ON T2M AND HARMONICITY”. International Electronic Journal of Geometry 6, no. 1 (April 2013): 100-111.
EndNote Mustapha D, Djaa NE, Nasrı R (April 1, 2013) NATURAL METRICS ON T2M AND HARMONICITY. International Electronic Journal of Geometry 6 1 100–111.
IEEE D. Mustapha, N. E. Djaa, and R. Nasrı, “NATURAL METRICS ON T2M AND HARMONICITY”, Int. Electron. J. Geom., vol. 6, no. 1, pp. 100–111, 2013.
ISNAD Mustapha, Djaa et al. “NATURAL METRICS ON T2M AND HARMONICITY”. International Electronic Journal of Geometry 6/1 (April 2013), 100-111.
JAMA Mustapha D, Djaa NE, Nasrı R. NATURAL METRICS ON T2M AND HARMONICITY. Int. Electron. J. Geom. 2013;6:100–111.
MLA Mustapha, Djaa et al. “NATURAL METRICS ON T2M AND HARMONICITY”. International Electronic Journal of Geometry, vol. 6, no. 1, 2013, pp. 100-11.
Vancouver Mustapha D, Djaa NE, Nasrı R. NATURAL METRICS ON T2M AND HARMONICITY. Int. Electron. J. Geom. 2013;6(1):100-11.