Let M̃ be an (m+r)-dimensional locally conformal Kähler (l.c.K.) manifold and let M be an m-dimensional l.c.K. submanifold of M̃ (i.e., a complex submanifold with the induced l.c.K. structure). Assume that both M̃ and M are pseudo-Bochner-flat. We prove that if r < m, then M is totally geodesic (in the Hermitian sense) in M̃. This is the l.c.K. version of Iwatani's result for Bochner-flat Kähler submanifolds.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm108-2-12,
author = {Koji Matsuo},
title = {Pseudo-Bochner-flat locally conformal K\"ahler submanifolds},
journal = {Colloquium Mathematicae},
volume = {107},
year = {2007},
pages = {305-315},
zbl = {1120.53033},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm108-2-12}
}
Koji Matsuo. Pseudo-Bochner-flat locally conformal Kähler submanifolds. Colloquium Mathematicae, Tome 107 (2007) pp. 305-315. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm108-2-12/