Geodesic
Pseudo-Bochner-flat locally conformal Kähler submanifolds
Koji Matsuo1
1 Department of Mathematics Ichinoseki National College of Technology Ichinoseki 021-8511, Japan
Colloquium Mathematicum, Tome 108 (2007) no. 2, pp. 305-315

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/cm108-2-12
Mots-clés : widetilde dimensional locally conformal hler manifold m dimensional submanifold widetilde complex submanifold induced structure assume widetilde pseudo bochner flat prove totally geodesic hermitian sense widetilde version iwatanis result bochner flat hler submanifolds

Koji Matsuo 1

1 Department of Mathematics Ichinoseki National College of Technology Ichinoseki 021-8511, Japan 
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Koji Matsuo. Pseudo-Bochner-flat locally conformal
 Kähler submanifolds. Colloquium Mathematicum, Tome 108 (2007) no. 2, pp. 305-315. doi: 10.4064/cm108-2-12

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