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NATURAL METRICS ON T2M AND HARMONICITY

Yıl 2013, Cilt: 6 Sayı: 1, 100 - 111, 30.04.2013

Djaa Mustapha Nour Elhouda Djaa Rafik Nasrı

Öz


Anahtar Kelimeler

Horizontal lift vertical lift natural metric λ-lift harmonic section

Kaynakça

  • [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.

Yıl 2013, Cilt: 6 Sayı: 1, 100 - 111, 30.04.2013

Djaa Mustapha Nour Elhouda Djaa Rafik Nasrı

Öz

Kaynakça

  • [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.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Djaa Mustapha Bu kişi benim

Nour Elhouda Djaa

Rafik Nasrı Bu kişi benim

Yayımlanma Tarihi 30 Nisan 2013
Yayımlandığı Sayı Yıl 2013 Cilt: 6 Sayı: 1

Kaynak Göster

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. Nisan 2013;6(1):100-111.
Chicago Mustapha, Djaa, Nour Elhouda Djaa, ve Rafik Nasrı. “NATURAL METRICS ON T2M AND HARMONICITY”. International Electronic Journal of Geometry 6, sy. 1 (Nisan 2013): 100-111.
EndNote Mustapha D, Djaa NE, Nasrı R (01 Nisan 2013) NATURAL METRICS ON T2M AND HARMONICITY. International Electronic Journal of Geometry 6 1 100–111.
IEEE D. Mustapha, N. E. Djaa, ve R. Nasrı, “NATURAL METRICS ON T2M AND HARMONICITY”, Int. Electron. J. Geom., c. 6, sy. 1, ss. 100–111, 2013.
ISNAD Mustapha, Djaa vd. “NATURAL METRICS ON T2M AND HARMONICITY”. International Electronic Journal of Geometry 6/1 (Nisan 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 vd. “NATURAL METRICS ON T2M AND HARMONICITY”. International Electronic Journal of Geometry, c. 6, sy. 1, 2013, ss. 100-11.
Vancouver Mustapha D, Djaa NE, Nasrı R. NATURAL METRICS ON T2M AND HARMONICITY. Int. Electron. J. Geom. 2013;6(1):100-11.