Submanifolds satisfying some curvature conditions imposed on the Weyl tensor

Abstract

In this paper we define Weyl semiparallel (C . h = 0) and Weyl 2-semiparallel (C . (&DEL;) over barh 0) submanifolds. We consider n-dimensional normally flat submanifolds satisfying these curvature conditions in (n + d)-dimensional Euclidean space En+d. We also consider normally flat submanifolds in (n + d)-dimensional Euclidean space En+d satisfying the condition C . h = LQ(g, h) and C . (&DEL;) over barh = LQ(g, (&DEL;) over barh).