Araştırma Makalesi
BibTex RIS Kaynak Göster

CONNECTIONS AND SECOND ORDER DIFFERENTIAL EQUATIONS ON INFINITE DIMENSIONAL MANIFOLDS

Yıl 2013, Cilt: 6 Sayı: 2, 45 - 56, 30.10.2013

Öz


Kaynakça

  • [1] Abbati, M.C. and Mania, A., On differential structure for projective limits of manifolds, J. Geom. Phys. 29(1999), 35-63.
  • [2] Aghasi, M., Dodson, C.T.J., Galanis, G.N. and Suri, A., Infinite dimensional second order ordinary differential equations via T 2M , J. Nonlinear Analysis. 67(2007), 2829-2838.
  • [3] Aghasi, M. and Suri, A., Ordinary differential equations on infinite dimensional manifolds, Balkan journal of geometry and its applications, 12(2007), No. 1, 1-8.
  • [4] Aghasi, M. and Suri, A., Splitting theorems for the double tangent bundles of Fr´echet mani- folds, Balkan journal of geometry and its applications, 15(2010), No.2, 1-13.
  • [5] Ashtekar, A. and Lewandowski, J., Differential geometry on the space of connections via graphs and projective limits, J. Geo. Phys., 17(1995), 191-230.
  • [6] Francesco, B. and Lewis A., Geometric control of mechanical systems, Springer, 2004.
  • [7] Del Riego, L. and Parker, P.E., Geometry of nonlinear connections, J. Nonlinear Analysis, 63(2005), 501-510.
  • [8] Eliasson, H. I., Geometry of manifolds of maps, J. Diff. Geo., 1(1967), 169-194.
  • [9] Galanis, G.N., Differential and Geometric Structure for the Tangent Bundle of a Projective Limit Manifold, Rendiconti del Seminario Matematico di Padova, 112(2004).
  • [10] Hamilton, R.S., The inverse functions theorem of Nash and Moser, Bull. of Amer. Math. Soc., 7(1982), 65-222.
  • [11] Klingenberg, W., Riemannian geometry, Walter de Gruyter, Berlin, 1995.
  • [12] Lang, S., Fundumentals of differential geometry, Graduate Texts in Mathematics, Vol. 191, Springer-Verlag, New York, 1999.
  • [13] Lee, J.M., Differential and physical geometry, Addison-Wesley, Reading Massachusetts, 1972.
  • [14] Mangiarotti, L. and Sardanashvily, G., Connections in classical and quantum field theory, World scientific.
  • [15] Müller, O., A metric approach to Fr´echet geometry, J. Geo. Phys., 58(2008), Issue 11, 1477- 1500.
  • [16] Omori, H., Infinite-dimensional Lie groups, Translations of Mathematical Monographs. 158. Berlin: American Mathematical Society (1997).
  • [17] Saunders, D.J., The geometry of jet bundles, Cambridge Univ. Press, Cambridge, 1989.
  • [18] Vilms, J., Connections on tangent bundles, J. Diff. Geom. 1(1967), 235-243.
Yıl 2013, Cilt: 6 Sayı: 2, 45 - 56, 30.10.2013

Öz

Kaynakça

  • [1] Abbati, M.C. and Mania, A., On differential structure for projective limits of manifolds, J. Geom. Phys. 29(1999), 35-63.
  • [2] Aghasi, M., Dodson, C.T.J., Galanis, G.N. and Suri, A., Infinite dimensional second order ordinary differential equations via T 2M , J. Nonlinear Analysis. 67(2007), 2829-2838.
  • [3] Aghasi, M. and Suri, A., Ordinary differential equations on infinite dimensional manifolds, Balkan journal of geometry and its applications, 12(2007), No. 1, 1-8.
  • [4] Aghasi, M. and Suri, A., Splitting theorems for the double tangent bundles of Fr´echet mani- folds, Balkan journal of geometry and its applications, 15(2010), No.2, 1-13.
  • [5] Ashtekar, A. and Lewandowski, J., Differential geometry on the space of connections via graphs and projective limits, J. Geo. Phys., 17(1995), 191-230.
  • [6] Francesco, B. and Lewis A., Geometric control of mechanical systems, Springer, 2004.
  • [7] Del Riego, L. and Parker, P.E., Geometry of nonlinear connections, J. Nonlinear Analysis, 63(2005), 501-510.
  • [8] Eliasson, H. I., Geometry of manifolds of maps, J. Diff. Geo., 1(1967), 169-194.
  • [9] Galanis, G.N., Differential and Geometric Structure for the Tangent Bundle of a Projective Limit Manifold, Rendiconti del Seminario Matematico di Padova, 112(2004).
  • [10] Hamilton, R.S., The inverse functions theorem of Nash and Moser, Bull. of Amer. Math. Soc., 7(1982), 65-222.
  • [11] Klingenberg, W., Riemannian geometry, Walter de Gruyter, Berlin, 1995.
  • [12] Lang, S., Fundumentals of differential geometry, Graduate Texts in Mathematics, Vol. 191, Springer-Verlag, New York, 1999.
  • [13] Lee, J.M., Differential and physical geometry, Addison-Wesley, Reading Massachusetts, 1972.
  • [14] Mangiarotti, L. and Sardanashvily, G., Connections in classical and quantum field theory, World scientific.
  • [15] Müller, O., A metric approach to Fr´echet geometry, J. Geo. Phys., 58(2008), Issue 11, 1477- 1500.
  • [16] Omori, H., Infinite-dimensional Lie groups, Translations of Mathematical Monographs. 158. Berlin: American Mathematical Society (1997).
  • [17] Saunders, D.J., The geometry of jet bundles, Cambridge Univ. Press, Cambridge, 1989.
  • [18] Vilms, J., Connections on tangent bundles, J. Diff. Geom. 1(1967), 235-243.
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Ali Surı Bu kişi benim

Mansour Aghası Bu kişi benim

Yayımlanma Tarihi 30 Ekim 2013
Yayımlandığı Sayı Yıl 2013 Cilt: 6 Sayı: 2

Kaynak Göster

APA Surı, A., & Aghası, M. (2013). CONNECTIONS AND SECOND ORDER DIFFERENTIAL EQUATIONS ON INFINITE DIMENSIONAL MANIFOLDS. International Electronic Journal of Geometry, 6(2), 45-56.
AMA Surı A, Aghası M. CONNECTIONS AND SECOND ORDER DIFFERENTIAL EQUATIONS ON INFINITE DIMENSIONAL MANIFOLDS. Int. Electron. J. Geom. Ekim 2013;6(2):45-56.
Chicago Surı, Ali, ve Mansour Aghası. “CONNECTIONS AND SECOND ORDER DIFFERENTIAL EQUATIONS ON INFINITE DIMENSIONAL MANIFOLDS”. International Electronic Journal of Geometry 6, sy. 2 (Ekim 2013): 45-56.
EndNote Surı A, Aghası M (01 Ekim 2013) CONNECTIONS AND SECOND ORDER DIFFERENTIAL EQUATIONS ON INFINITE DIMENSIONAL MANIFOLDS. International Electronic Journal of Geometry 6 2 45–56.
IEEE A. Surı ve M. Aghası, “CONNECTIONS AND SECOND ORDER DIFFERENTIAL EQUATIONS ON INFINITE DIMENSIONAL MANIFOLDS”, Int. Electron. J. Geom., c. 6, sy. 2, ss. 45–56, 2013.
ISNAD Surı, Ali - Aghası, Mansour. “CONNECTIONS AND SECOND ORDER DIFFERENTIAL EQUATIONS ON INFINITE DIMENSIONAL MANIFOLDS”. International Electronic Journal of Geometry 6/2 (Ekim 2013), 45-56.
JAMA Surı A, Aghası M. CONNECTIONS AND SECOND ORDER DIFFERENTIAL EQUATIONS ON INFINITE DIMENSIONAL MANIFOLDS. Int. Electron. J. Geom. 2013;6:45–56.
MLA Surı, Ali ve Mansour Aghası. “CONNECTIONS AND SECOND ORDER DIFFERENTIAL EQUATIONS ON INFINITE DIMENSIONAL MANIFOLDS”. International Electronic Journal of Geometry, c. 6, sy. 2, 2013, ss. 45-56.
Vancouver Surı A, Aghası M. CONNECTIONS AND SECOND ORDER DIFFERENTIAL EQUATIONS ON INFINITE DIMENSIONAL MANIFOLDS. Int. Electron. J. Geom. 2013;6(2):45-56.