Pseudo-Bochner-flat locally conformal Kähler submanifolds
Tom 108 / 2007
Colloquium Mathematicum 108 (2007), 305-315 MSC: 53C55, 53C40. DOI: 10.4064/cm108-2-12
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.