On pseudo-harmonic maps in conformal geometry

Abstract

We extend harmonic map techniques to the setting of more general differential equations in conformal geometry. We obtain an extension of Siu's rigidity to Kahler-Weyl geometry and apply the latter to Vaisman's conjecture. Other applications include topological obstructions to the existence of Kahler-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 Kahler-Weyl manifold of certain type.

errors corrected, revised versions of the results, the proof of the factorisation theorem is re-written, references updated, 32 pages

References in corpus (2)

• On pseudo-harmonic maps in conformal geometry
• Locally conformally Kähler manifolds. A selection of results

Cited by in corpus (13)

• On pseudo-harmonic maps in conformal geometry
• LCK rank of locally conformally Kahler manifolds with potential
• Fibrations and fundamental groups of Kaehler-Weyl manifolds
• Topology of steady and expanding gradient Ricci solitons via f-harmonic maps
• The deficiencies of Kaehler groups
• Hopf surfaces in locally conformally Kahler manifolds with potential
• Homogeneous locally conformally Kähler manifolds
• On pluricanonical locally conformally Kähler manifolds
• On $(H,\tilde{H})$-harmonic Maps between pseudo-Hermitian manifolds
• Hermitian Harmonic maps and non-degenerate curvatures
• Locally conformally symplectic structures on compact non-Kähler complex surfaces
• Topology of locally conformally Kahler manifolds with potential
• Pseudo-harmonic Hermitian structures on Weyl manifolds