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Abstract

Let $\widetilde M$ be an $(m+r)$-dimensional locally conformal Kähler (l.c.K.) manifold and let $M$ be an $m$-dimensional l.c.K. submanifold of $\widetilde M$ (i.e., a complex submanifold with the induced l.c.K. structure). Assume that both $\widetilde M$ and $M$ are pseudo-Bochner-flat. We prove that if $r < m$, then $M$ is totally geodesic (in the Hermitian sense) in $\widetilde M$. This is the l.c.K. version of Iwatani's result for Bochner-flat Kähler submanifolds.