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Transactions of the American Mathematical Society

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Connections with prescribed first Pontrjagin form


Author: Mahuya Datta
Journal: Trans. Amer. Math. Soc. 355 (2003), 3813-3824
MSC (2000): Primary 53C05, 53C23, 58J99
DOI: https://doi.org/10.1090/S0002-9947-03-03311-7
Published electronically: May 15, 2003
MathSciNet review: 1990175
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $P$ be a principal $O(n)$ bundle over a $C^\infty$manifold $M$ of dimension $m$. If $n\geq 5m+4+4\binom{m+1}{4}$, then we prove that every differential 4-form representing the first Pontrjagin class of $P$ is the Pontrjagin form of some connection on $P$.


References [Enhancements On Off] (What's this?)

  • 1. M. Datta, A note on Pontrjagin forms, Proceedings of the American Mathematical Society 128 (2000), pp. 3723 - 3729. MR 2001k:53142
  • 2. M. Gromov, Partial Differential Relations, Ergebnisse der Mathematik und ihrer Grenzgebiete 3. Folge Band 9. Springer-Verlag, Berlin, 1986. MR 90a:58201
  • 3. S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vols. I, II, Interscience Tracts in Pure and Applied Mathematics, John Wiley and Sons, 1963, 1969. MR 27:2945; MR 38:6501

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Additional Information

Mahuya Datta
Affiliation: Department of Pure Mathematics, University of Calcutta, 35 P. Barua Sarani, Calcutta 700019, India
Email: mahuyad@hotmail.com

DOI: https://doi.org/10.1090/S0002-9947-03-03311-7
Keywords: Principal bundle, connections, first Pontrjagin form
Received by editor(s): September 26, 2002
Received by editor(s) in revised form: February 14, 2003
Published electronically: May 15, 2003
Article copyright: © Copyright 2003 American Mathematical Society

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