Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-24T23:50:28.632Z Has data issue: false hasContentIssue false
  • English
  • Français

The eigenforms of the complex Laplacian for a Hermitian submersion

Published online by Cambridge University Press:  22 January 2016

Peter B. Gilkey ,
John V. Leahy  and
JeongHyeong Park
Peter B. Gilkey
Affiliation:
Mathematics Department, University of Oregon Eugene, OR 97403, USA, [email protected]
John V. Leahy
Affiliation:
Mathematics Department, University of Oregon Eugene, OR 97403, USA, [email protected]
JeongHyeong Park
Affiliation:
Department of Mathematics, Honam University, Seobongdong 59, Kwangsanku, Kwangju, 506-090, South Korea, [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let π : Z → Y be a Hermitian submersion. We study when the pull-back of an eigenform of the complex Laplacian on Y is an eigenform of the complex Laplacian on Z.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 156 , 1999 , pp. 1 - 23
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1999

References

[1] Bergery, Berard L. and Bourguignon, J. P., Laplacians and Riemannian submersions with totally geodesic fibers, Illinois J Math, 26 (1982), 181–200.Google Scholar
[2] Burstall, F., Non-linear functional analysis and harmonic maps, Ph D Thesis (Warwick).Google Scholar
[3] Gilkey, P. B., Invariance Theory, the Heat Equation, and the Atiyah-Singer Index theorem (2nd edition), ISBN 0–8493-7874–4, CRC Press, Boca Raton, Florida, 1994.Google Scholar
[4] Gilkey, P. B., Leahy, J. V., and Park, J. H., The spectral geometry of the Hopf fibration, Journal Physics A, 29 (1996), 5645–5656.Google Scholar
[5] Gilkey, P. B., Eigenvalues of the form valued Laplacian for Riemannian submersions., Proc. AMS, 126 (1998), 1845–1850.Google Scholar
[6] Gilkey, P. B., Eigenforms of the spin Laplacian and projectable spinors for principal bun dles., J. Nucl. Phys. B., 514 [PM] (1998), 740–752.CrossRefGoogle Scholar
[7] Gilkey, P. B. and Park, J. H., Riemannian submersions which preserve the eigenforms of the Laplacian, Illinois J Math, 40 (1996), 194–201.Google Scholar
[8] Goldberg, S. I. and Ishihara, T., Riemannian submersions commuting with the Laplacian, J. Diff. Geo., 13 (1978), 139–144.Google Scholar
[9] Gudmundsson, S., The Bibliography of Harmonic Morphisms, (Available on the internet at http://www.maths.lth.se/matematiklu/personal/sigma/harmonic/bibliography.html).Google Scholar
[10] Johnson, D. L., Kaehler submersions and holomorphic connections, J. Diff. Geo., 15 (1980), 71–79.Google Scholar
[11] Muto, Y., Some eigenforms of the Laplace-Beltrami operators in a Riemannian submersion, J. Korean Math. Soc, 15 (1978), 39–57.Google Scholar
[12] Muto, Y., Riemannian submersion and the Laplace-Beltrami operator, Kodai Math J., 1 (1978), 329–338.Google Scholar
[13] Park, J. H., The Laplace-Beltrami operator and Riemannian submersion with minimal and not totally geodesic fibers, Bull. Korean Math. Soc, 27 (1990), 39–47.Google Scholar
[14] Watson, B., Manifold maps commuting with the Laplacian, J. Diff. Geo., 8 (1973), 85–94.Google Scholar
[15] Watson, B., Almost Hermitian submersions, J. Diff. Geo., 11 (1976), 147–165.Google Scholar