On Generic submanifolds of a locally conformal Kahler manifold with parallel canonical structures

摘要

The study ofCR-submanifolds of a Kähler manifold wasinitiated by Bejancu [1]. Since then many papers have appeared onCR-submanifolds of a Kähler manifold. Also, it has been studied thatgeneric submanifolds of Kähler manifolds [2] are generalisations ofholomorphic submanifolds, totally real submanifolds andCR-submanifolds of Kähler manifolds. On the other hand, many examplesC2of generic surfaces in which are notCR-submanifolds have beengiven by Chen [3] and this leads to the present paper where we obtainsome necessary conditions for a generic submanifolds in a locallyconformal Kähler manifold with four canonical strucrures, denoted byP,F,tandf, to have parallelP,Fandt. We also prove that for ageneric submanifold of a locally conformal Kähler manifold,Fisparallel ifftis parallel.