Abstract
We show that any harmonic (with respect to the Bergman metric) vector field tangent to the Levi distribution of the foliation by level sets of the defining function φ ( z ) = − K ( z , z ) − 1 / ( n + 1 ) of a strictly pseudoconvex bounded domain Ω ⊂ C n which is smooth up to the boundary must vanish on ∂ Ω . If n ≠ 5 and u T is a harmonic vector field with u ∈ C 2 ( Ω ¯ ) then u | ∂ Ω = 0 .
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