Abstract
The theory of harmonic vector fields on Riemannian manifolds is generalised to pseudo-Riemannian manifolds. The congruence structure of conformal gradient fields on pseudo-Riemannian hyperquadrics and Killing fields on pseudo-Riemannian quadrics is elucidated, and harmonic vector fields of these two types are classified up to congruence. A para-Kähler twisted anti-isometry is used to correlate harmonic vector fields on the quadrics of neutral signature.
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