SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2021 / Volume: 50 Issue: 6

A note on induced connections

Mohamed Tahar Kadaoui Abbassi(Sidi Mohamed Benabdellah University)0000-0001-7802-0624
Ibrahim Lakrini(Sidi Mohamed Ben Abdallah University)0000-0001-9863-8886
Pages
—
Publication Date
2021-12-14
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Consequently, we give the expression of the curvature in terms of the curvature 2-form of a connection on a principal bundle.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this note, we will exploit the classical bijective correspondence between sections of an associated vector bundle and equivariant functions on the underlying principal bundle to revisit a global formula for induced connections on associated vector bundles.
📊
Key Findings & Data:In this note, we will exploit the classical bijective correspondence between sections of an associated vector bundle and equivariant functions on the underlying principal bundle to revisit a global formula for induced connections on associated vector bundles.
💡
Conclusion & Impact:Consequently, we give the expression of the curvature in terms of the curvature 2-form of a connection on a principal bundle.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Principal bundle · Assosiated bundle · Induced connection

Abstract

In this note, we will exploit the classical bijective correspondence between sections of an associated vector bundle and equivariant functions on the underlying principal bundle to revisit a global formula for induced connections on associated vector bundles. Consequently, we give the expression of the curvature in terms of the curvature 2-form of a connection on a principal bundle.

🔖

Cite This Article

Abbassi, M. T. K., Lakrini, I. (2021). A note on induced connections. Hacettepe Journal of Mathematics and Statistics, Volume: 50 Issue: 6. https://doi.org/10.15672/hujms.829790

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (16)

  1. M. Daniel and C.M. Viallet, The geometrical setting of gauge theories of the Yang- Mills type, Reviews of modern physics, 52(1), 175–197, 1980.
  2. M. Göckeler and T. Schucker, Differential geometry, Gauge theories and gravity, Cam- bridge Monographs on Mathematical Physics, Cambridge Univ. Press, 1987.
  3. W. Greub, S. Halperin and R. Vanstone, Connections, Curvature and Cohomology, Vol. 1, Academic Press, New York and London, 1972.
  4. R. Healey, Gauging what’s real: the conceptual foundations of contemporary gauge theories, Oxford University Press, New York, 2007.
  5. C.J. Isham, Modern Differential Geometry For Physicists, World Scientific, 2003.
  6. T.A. Ivey and J.M. Landsberg, Cartan for beginners: differential geometry via moving frames and exterior differential systems, Graduate studies in Maths. 61, AMS Providence Rhode Island, 2003.
  7. S. Kobayashi and K. Nomizu, Foundations of differential geometry, Vol.1, Interscience Publishers, New York and London, 1963.
  8. I. Kolàr, P. Michor and J. Slovak, Natural operations in differential geometry, Springer-Verlag, Berlin Heidelberg, 1993.
  9. K. Nomizu, Lie Groups and Differential Geometry, Mathematical Society of Japan, 1954.
  10. W.A. Poor, Differential geometric structures, Dover Pubs. Inc. Mineola, New York, 2007.
  11. G. Rudolph and M. Schmidt, Differential geometry and mathematical physics. Part 1, Springer, 2013.
  12. R.W. Sharpe, Differential geometry: Cartan’s generalization of Klein Erlangen program, GTM 166, Springer, New York, 2000.
  13. M. Spivak, A comprehensive introduction to differential geometry II, Publish or Perish Inc., Houston, 1979.
  14. S. Sternberg, Lectures on Differential Geometry, AMS Chelsea, 1983.
  15. C.M. Wood, An existence theorem for harmonic sections, Manuscr. Math. 68, 69–75, 1990.
  16. K. Nomizu, Lie Groups and Differential Geometry, Mathematical Society of Japan, 1954.