Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-28T13:10:16.973Z Has data issue: false hasContentIssue false
  • English
  • Français

Harmonic morphisms from homogeneous spaces of positive curvature

Published online by Cambridge University Press:  28 July 2014

SIGMUNDUR GUDMUNDSSON  and
MARTIN SVENSSON
SIGMUNDUR GUDMUNDSSON
Affiliation:
Department of Mathematics, Faculty of Science, Lund University, Box 118, S-22100 Lund, Sweden. e-mail: [email protected]
MARTIN SVENSSON
Affiliation:
Department of Mathematics & Computer Science, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark. e-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We prove local existence of complex-valued harmonic morphisms from any Riemannian homogeneous space of positive curvature, except the Berger space Sp(2)/SU(2).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 157 , Issue 2 , September 2014 , pp. 321 - 327
Copyright
Copyright © Cambridge Philosophical Society 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Aloff, S. and Wallach, N. R.An infinite family of distinct 7-manifolds admitting positively curved Riemannian structures, Bull. Amer. Math. Soc. 81 (1975), 93–97.CrossRefGoogle Scholar
[2]Baird, P. and Eells, J.A Conservation Law for Harmonic Maps. Geometry Symposium Utrecht 1980. Lecture Notes in Math. vol. 894, (Springer 1981), pp. 1–25.Google Scholar
[3]Baird, P. and Wood, J. C.Harmonic Morphisms Between Riemannian Manifolds. London Math. Soc. Monogr. No. 29 (Oxford University Press, 2003).CrossRefGoogle Scholar
[4]Bérard–Bergery, L.Sur certaines fibrations d'espaces homogénes riemanniens. Compositio Math. 30 (1975), 43–61.Google Scholar
[5]Bérard–Bergery, L.Les variétés riemanniennes homogénes simplement connexes de dimension impaire á courbure strictement positive. J. Math. Pures Appl. (9) 55 (1976), 47–67.Google Scholar
[6]Berger, M.Les variétés riemanniennes homogénes normales simplement connexes á courbure strictement positive. Ann. Scuola Norm. Sup. Pisa. (3) 15 (1961), 179–246.Google Scholar
[7]Besse, A. L.Einstein Manifolds. Ergeb. Math. Grenzgeb. (3) 10 (Springer-Verlag, 1987).Google Scholar
[8]Elíasson, H. I.Die Krümmung des Raumes Sp2/SU2 von Berger. Math. Ann. 164 (1966), 317–323.CrossRefGoogle Scholar
[9]Fuglede, B.Harmonic morphisms between Riemannian manifolds. Ann. Inst. Fourier 28 (1978), 107–144.CrossRefGoogle Scholar
[10]Gudmundsson, S.The Bibliography of Harmonic Morphisms. http://www.matematik.lu.se/matematiklu/personal/sigma/harmonic/bibliography.html.Google Scholar
[11]Gudmundsson, S.Harmonic morphisms from complex projective spaces. Geom. Dedicata 53 (1994), 155–161.CrossRefGoogle Scholar
[12]Gudmundsson, S. and Svensson, M.Harmonic morphisms from solvable Lie groups. Math. Proc. Camb. Phil. Soc. 147 (2009), 389–408.CrossRefGoogle Scholar
[13]Ishihara, T.A mapping of Riemannian manifolds which preserves harmonic functions. J. Math. Soc. Japan 7 (1979), 345–370.Google Scholar
[14]Wallach, N. R.Compact homogeneous Riemannian manifolds with strictly positive curvature. Ann. of Math. (2) 96 (1972), 277–295.CrossRefGoogle Scholar
[15]Wilking, B.The normal homogeneous space (SU(3) × SO(3))/US*(2) has positive sectional curvature. Proc. Amer. Math. Soc. 127 (1999), 1191–1194.CrossRefGoogle Scholar
[16]Ziller, W.Examples of Riemannian Manifolds with Non-Negative Sectional Curvature. Surveys Differ. Geom. XI, 63102 (Int. Press, Somerville, MA, 2007).Google Scholar