Otoba, Nobuhiko and Petean, Jimmy (2020) Bifurcation for the Constant Scalar Curvature Equation and Harmonic Riemannian Submersions. JOURNAL OF GEOMETRIC ANALYSIS, 30 (4). pp. 4453-4463. ISSN 1050-6926, 1559-002X
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We study bifurcation for the constant scalar curvature equation along a one-parameter family of Riemannian metrics on the total space of a harmonic Riemannian submersion. We provide an existence theorem for bifurcation points and a criterion to see that the conformal factors corresponding to the bifurcated metrics must be indeed constant along the fibers. In the case of the canonical variation of a Riemannian submersion with totally geodesic fibers, we characterize discreteness of the set of all degeneracy points along the family and give a sufficient condition to guarantee that bifurcation necessarily occurs at every point where the linearized equation has a nontrivial solution. In the model case of quaternionic Hopf fibrations, we show that SU(2)-symmetry-breaking bifurcation does not occur except at the round metric.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | YAMABE PROBLEM; DIFFERENTIAL-EQUATIONS; METRICS; THEOREM; Constant scalar curvature; Bifurcation for potential operators; Symmetry-breaking bifurcation; Horizontal Laplacian; Canonical variation; Riemannian submersion with totally geodesic fibers; Hopf fibrations |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics Mathematics > Prof. Dr. Bernd Ammann |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 08 Mar 2021 07:30 |
| Last Modified: | 08 Mar 2021 07:30 |
| URI: | https://pred.uni-regensburg.de/id/eprint/43311 |
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