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Proceedings of the London Mathematical Society Advance Access originally published online on February 5, 2009
Proceedings of the London Mathematical Society 2009 99(1):168-194; doi:10.1112/plms/pdn056
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© 2009 London Mathematical Society

On pseudo-harmonic maps in conformal geometry

Gerasim Kokarev

School of Mathematics
The University of Edinburgh
King's Buildings
Mayfield Road
Edinburgh
EH9 3JZ
United Kingdom

Received 15 June 2007.

We extend harmonic map techniques to the setting of more general differential equations in conformal geometry. We discuss existence theorems and obtain an extension of Siu's strong rigidity to Kähler–Weyl geometry. Other applications include topological obstructions to the existence of Kähler–Weyl structures. For example, we show that no co-compact lattice in SO(1, n), n > 2, can be the fundamental group of a compact Kähler–Weyl manifold of certain type.

2000 Mathematics Subject Classification 53C43, 53C44, 53C55.

This work is supported by EPSRC.


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