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Bundle of Frames and Sprays for Fréchet Manifolds

Year 2018, Volume: 11 Issue: 1, 1 - 16, 30.04.2018
https://doi.org/10.36890/iejg.545066

Abstract

References

  • [1] Aghasi, M., Bahari, A.R., Dodson, C.T.J., Galanis, G.N. and Suri, A., Second order structures for sprays and connections on Fréchet manifolds. http://arxiv.org/abs/0810.5261v1.
  • [2] Aghasi,Mand Suri, A., Splitting theorems for the double tangent bundles of Fréchet manifolds. Balkan J. Geom. Appl. 15 (2010), no. 2, 1-13.
  • [3] Antonelli, P.L., Ingarden, R.S. and Matsumoto, M.S., The Theory of Sprays and Finsler Spaces with Applications in Physics and Biology. Kluwer, Dordrecht, 1993.
  • [4] Ashtekar, A., and Isham, C.J., Representations of the holonomy algebras of gravity and non-Abelian gauge theories. Classical Quantum Gravity, 9 (1992), 1433-1467.
  • [5] Ashtekar, A. and Lewandowski, J., Differential geometry on the space of connections via graphs and projective limits. J. Geom. Phys., 17 (1995), 191-230.
  • [6] Bourbaki, N., Varietés differentielles et analytiques. Fascisule de résultats 1-7, Herman, Paris, 1967.
  • [7] Dodson, C.T.J. and Galanis, G.N., Bundles of acceleration on Banach manifolds. World Congress of Nonlinear Analysis, June 30 July 7, Orlando, 2004.
  • [8] Dodson, C.T.J., Galanis, G.N., Vassiliou, E., A generalized second order frame bundle for Fréchet manifolds. J. Geom. Phys. 55, (2005), no. 3, 291-305.
  • [9] Eliasson, H.I., Geometry of manifolds of maps. J. Diff. Geom. 1 (1967), pp. 169-194.
  • [10] Galanis, G.N., Differential and Geometric Structure for the Tangent Bundle of a Projective Limit Manifold. Rendiconti del Seminario Matematico di Padova. 112 (2004), 1-12.
  • [11] Galanis, G.N., Projective limits of Banach vector bundles. Portugaliae Mathematica 55 (1998), no. 1, 11-24.
  • [12] Hamilton, R.S., The inverse functions theorem of Nash and Moser. Bull. Amer. Math. Soc., 7 (1982), 65-222.
  • [13] Klingenberg, W., Riemannian geometry. de Gruyter, Berlin, 1982.
  • [14] Lang, S., Fundumentals of differential geometry. Graduate Texts in Mathematics, vol. 191, Springer-Verlag, New York, 1999.
  • [15] Mangiarotti, L., Sardanashvily, G., Connections in classical and quantum field theory. World Scientific, 2000.
  • [16] Kriegl, A. and Michor, P., The convenient setting of global analysis. Mathematical Surveys and Monographs, 53 American Mathematical Society, 1997.
  • [17] Nag, S., The complex analytic theory of the Teichmulller spaces. J. Wiley, New York, 1988.
  • [18] Nag, S. and Sullivan, D., Teichmulller theory and the universal period mapping via quantum calculus and the H1=2 space on the circle. Osaka J. Math. 32 (1995), 1-34.
  • [19] Muller, O., A metric approach to Fréchet geometry. J. Geom. Phys. 58 (2008), no. 11, 1477-1500.
  • [20] Omori, H., Infinite-dimensional Lie groups. Translations of Mathematical Monographs. 158. Berlin: American Mathematical Society, 1997.
  • [21] Saunders, D.J., The geometry of jet bundles. Cambridge Univ. Press, Cambridge, 1989.
  • [22] Suri, A. and Aghasi, M., Connections and second order differential equations on infinite dimensional manifolds Int. Elect. J. Geom. 6 (2013), no. 2, 45-56.
  • [23] Suri, A., Higher order frame bundles. Balkan J. Geom. Appl. 21 (2016), no. 2, 102-117.
  • [24] Suri, A. and Rastegarzadeh, S., Complete Lift of Vector fields and Sprays to T1M. Int. J. Geom. Methods Mod. Phys. 12 (2015), 1550113.
  • [25] Vassiliou, E., Transformations of linear connections. Period. Math. Hungar. 13 (1982), no. 4, 289-308.
  • [26] Vilms, J., Connections on tangent bundles. J. Diff. Geom. 1 (1967), 235-243.
Year 2018, Volume: 11 Issue: 1, 1 - 16, 30.04.2018
https://doi.org/10.36890/iejg.545066

Abstract

References

  • [1] Aghasi, M., Bahari, A.R., Dodson, C.T.J., Galanis, G.N. and Suri, A., Second order structures for sprays and connections on Fréchet manifolds. http://arxiv.org/abs/0810.5261v1.
  • [2] Aghasi,Mand Suri, A., Splitting theorems for the double tangent bundles of Fréchet manifolds. Balkan J. Geom. Appl. 15 (2010), no. 2, 1-13.
  • [3] Antonelli, P.L., Ingarden, R.S. and Matsumoto, M.S., The Theory of Sprays and Finsler Spaces with Applications in Physics and Biology. Kluwer, Dordrecht, 1993.
  • [4] Ashtekar, A., and Isham, C.J., Representations of the holonomy algebras of gravity and non-Abelian gauge theories. Classical Quantum Gravity, 9 (1992), 1433-1467.
  • [5] Ashtekar, A. and Lewandowski, J., Differential geometry on the space of connections via graphs and projective limits. J. Geom. Phys., 17 (1995), 191-230.
  • [6] Bourbaki, N., Varietés differentielles et analytiques. Fascisule de résultats 1-7, Herman, Paris, 1967.
  • [7] Dodson, C.T.J. and Galanis, G.N., Bundles of acceleration on Banach manifolds. World Congress of Nonlinear Analysis, June 30 July 7, Orlando, 2004.
  • [8] Dodson, C.T.J., Galanis, G.N., Vassiliou, E., A generalized second order frame bundle for Fréchet manifolds. J. Geom. Phys. 55, (2005), no. 3, 291-305.
  • [9] Eliasson, H.I., Geometry of manifolds of maps. J. Diff. Geom. 1 (1967), pp. 169-194.
  • [10] Galanis, G.N., Differential and Geometric Structure for the Tangent Bundle of a Projective Limit Manifold. Rendiconti del Seminario Matematico di Padova. 112 (2004), 1-12.
  • [11] Galanis, G.N., Projective limits of Banach vector bundles. Portugaliae Mathematica 55 (1998), no. 1, 11-24.
  • [12] Hamilton, R.S., The inverse functions theorem of Nash and Moser. Bull. Amer. Math. Soc., 7 (1982), 65-222.
  • [13] Klingenberg, W., Riemannian geometry. de Gruyter, Berlin, 1982.
  • [14] Lang, S., Fundumentals of differential geometry. Graduate Texts in Mathematics, vol. 191, Springer-Verlag, New York, 1999.
  • [15] Mangiarotti, L., Sardanashvily, G., Connections in classical and quantum field theory. World Scientific, 2000.
  • [16] Kriegl, A. and Michor, P., The convenient setting of global analysis. Mathematical Surveys and Monographs, 53 American Mathematical Society, 1997.
  • [17] Nag, S., The complex analytic theory of the Teichmulller spaces. J. Wiley, New York, 1988.
  • [18] Nag, S. and Sullivan, D., Teichmulller theory and the universal period mapping via quantum calculus and the H1=2 space on the circle. Osaka J. Math. 32 (1995), 1-34.
  • [19] Muller, O., A metric approach to Fréchet geometry. J. Geom. Phys. 58 (2008), no. 11, 1477-1500.
  • [20] Omori, H., Infinite-dimensional Lie groups. Translations of Mathematical Monographs. 158. Berlin: American Mathematical Society, 1997.
  • [21] Saunders, D.J., The geometry of jet bundles. Cambridge Univ. Press, Cambridge, 1989.
  • [22] Suri, A. and Aghasi, M., Connections and second order differential equations on infinite dimensional manifolds Int. Elect. J. Geom. 6 (2013), no. 2, 45-56.
  • [23] Suri, A., Higher order frame bundles. Balkan J. Geom. Appl. 21 (2016), no. 2, 102-117.
  • [24] Suri, A. and Rastegarzadeh, S., Complete Lift of Vector fields and Sprays to T1M. Int. J. Geom. Methods Mod. Phys. 12 (2015), 1550113.
  • [25] Vassiliou, E., Transformations of linear connections. Period. Math. Hungar. 13 (1982), no. 4, 289-308.
  • [26] Vilms, J., Connections on tangent bundles. J. Diff. Geom. 1 (1967), 235-243.
There are 26 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Ali Suri This is me

Mohammad Moosaei

Publication Date April 30, 2018
Published in Issue Year 2018 Volume: 11 Issue: 1

Cite

APA Suri, A., & Moosaei, M. (2018). Bundle of Frames and Sprays for Fréchet Manifolds. International Electronic Journal of Geometry, 11(1), 1-16. https://doi.org/10.36890/iejg.545066
AMA Suri A, Moosaei M. Bundle of Frames and Sprays for Fréchet Manifolds. Int. Electron. J. Geom. April 2018;11(1):1-16. doi:10.36890/iejg.545066
Chicago Suri, Ali, and Mohammad Moosaei. “Bundle of Frames and Sprays for Fréchet Manifolds”. International Electronic Journal of Geometry 11, no. 1 (April 2018): 1-16. https://doi.org/10.36890/iejg.545066.
EndNote Suri A, Moosaei M (April 1, 2018) Bundle of Frames and Sprays for Fréchet Manifolds. International Electronic Journal of Geometry 11 1 1–16.
IEEE A. Suri and M. Moosaei, “Bundle of Frames and Sprays for Fréchet Manifolds”, Int. Electron. J. Geom., vol. 11, no. 1, pp. 1–16, 2018, doi: 10.36890/iejg.545066.
ISNAD Suri, Ali - Moosaei, Mohammad. “Bundle of Frames and Sprays for Fréchet Manifolds”. International Electronic Journal of Geometry 11/1 (April 2018), 1-16. https://doi.org/10.36890/iejg.545066.
JAMA Suri A, Moosaei M. Bundle of Frames and Sprays for Fréchet Manifolds. Int. Electron. J. Geom. 2018;11:1–16.
MLA Suri, Ali and Mohammad Moosaei. “Bundle of Frames and Sprays for Fréchet Manifolds”. International Electronic Journal of Geometry, vol. 11, no. 1, 2018, pp. 1-16, doi:10.36890/iejg.545066.
Vancouver Suri A, Moosaei M. Bundle of Frames and Sprays for Fréchet Manifolds. Int. Electron. J. Geom. 2018;11(1):1-16.