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CONNECTIONS AND SECOND ORDER DIFFERENTIAL EQUATIONS ON INFINITE DIMENSIONAL MANIFOLDS

Year 2013, Volume: 6 Issue: 2, 45 - 56, 30.10.2013

Abstract


References

  • [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.
Year 2013, Volume: 6 Issue: 2, 45 - 56, 30.10.2013

Abstract

References

  • [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.
There are 18 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Ali Surı This is me

Mansour Aghası This is me

Publication Date October 30, 2013
Published in Issue Year 2013 Volume: 6 Issue: 2

Cite

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. October 2013;6(2):45-56.
Chicago Surı, Ali, and Mansour Aghası. “CONNECTIONS AND SECOND ORDER DIFFERENTIAL EQUATIONS ON INFINITE DIMENSIONAL MANIFOLDS”. International Electronic Journal of Geometry 6, no. 2 (October 2013): 45-56.
EndNote Surı A, Aghası M (October 1, 2013) CONNECTIONS AND SECOND ORDER DIFFERENTIAL EQUATIONS ON INFINITE DIMENSIONAL MANIFOLDS. International Electronic Journal of Geometry 6 2 45–56.
IEEE A. Surı and M. Aghası, “CONNECTIONS AND SECOND ORDER DIFFERENTIAL EQUATIONS ON INFINITE DIMENSIONAL MANIFOLDS”, Int. Electron. J. Geom., vol. 6, no. 2, pp. 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 (October 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 and Mansour Aghası. “CONNECTIONS AND SECOND ORDER DIFFERENTIAL EQUATIONS ON INFINITE DIMENSIONAL MANIFOLDS”. International Electronic Journal of Geometry, vol. 6, no. 2, 2013, pp. 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.