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Abstrakty
We directly prove that the foliation of the sphere S2n+1, the leaves of which are intersections of all complex linear 2-dimensional subspaces of Cn+1 translated by a constant vector p, defines a submersion that is horizontally conformal if and only if p = 0. We generalise this result to the cases of S4n+3 and S15 with foliations constructed using quaternionic and octonionic structure (resp.) in an analogous way.
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Czasopismo
Rocznik
Tom
Strony
738--747
Opis fizyczny
Bibliogr. 5 poz.
Twórcy
autor
- Faculty of Mathematics and Computer Sciences, University of Łódź, Banacha 22, 90-238 Łódź, Poland
Bibliografia
- [1] F. E. Burstall, D. Ferus, K. Leschke, F. Pedit, U. Pinkall, Conformal Geometry of Surfaces in S4 and Quaternions, Springer, Berlin, 2002.
- [2] D. B. A. Epstein, Foliations with all leaves compact, Ann. Inst. Fourier 26(1) (1976), 265–282.
- [3] R. H. Escobales Jr, Riemannian submersions with totally geodesic fibers, J. Differential Geom. 10(2) (1975), 253–276.
- [4] S. G. Heller, Conformal fibrations of S3 by circles, in Harmonic maps and differential geometry, 195–202, Contemp. Math. 542, AMS, Providence, R. I., 2011.
- [5] B. O’Neill, The fundamental equations of a submersion, Michigan Math. J. 13 (1966), 459–469.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-2d9bf3af-ff45-46fd-b635-58927f2268b0