Let D be a domain over a product space of a Stein manifold S and Grassmann manifolds G1 (i=1,2,...,N) and D be the envelope of holomorphy of D. In this paper we shall show that each real-valued pluriharmonic function on D is the real part of a holomorphic function on D if and only if H1 (D, Z)=0, provided that D is not holomorphically equivalent to the set E×V1×...×Vi-1×G1×Vi+1×...×VN (i=1,...,N), where E is an open set of S and Vi is an open set of Gi.
Pluriharmonic Functions on a Domain over a Product Space
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