Examples of non-conformal submersions from spheres with umbilical fibers

• Autorzy: Zawadzki T.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

foliation; conformal submersion; spheres

PL

kule

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2014
• Tom: Vol. 47, nr 3
• Strony: 738--747
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Zawadzki T.

• 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.