• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.325-332
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• 1997

Let $Z = X \times Y$ where X and Y are complex manifolds. We suppose that projection $\pi$ on the second factor is a Riemannian submersion, that TX is perpendicular to TY, and that the metrics on Z and on Y are Hermetian; we do not assume Z is a Riemannian product. We study when the pull-back of an eigenfunction of the complex Laplacian on Y is an eigenfunction of the complex Laplacian on Z.

• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.669-670
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• 1994

Let $E \to M$ be a hermitian holomorphic vector bundle over a compact (complex) hermitian manifold M of complex dimension n, and let $$ d"_p(E) : 0 \to A^{p,0}(E) \to A^{p,1}(E) \to \cdots \to A^{p,n}(E) \to 0$$ be the Dolbeault complex. Then $A^{p,q}(E)$ become a prehibert space so that the formal adjoint $\delta"$ of $d"$ and the "Laplacian" $\Delta" = \delta" d" + d" \delta"$ are defined.quot; d" + d" \delta"$ are defined.;$ are defined.