Abstract. We study some functions de ned on the unit tangent space, which are formedwith the second fundamental form of submanifolds of a real space form. These give anexact expression of isotropy of submanifolds in a real space form and a relationship betweenintrinsic invariants and extrinsic ones. 1. IntroductionThe relationship between intrinsic and extrinsic invariants of submanifolds inEuclidean space or a space form is very interesting for geometers. One example foran obstruction to minimal isometric immersions into Euclidean space is that theRicci curvature takes non-negative values. On the other hand, Chen ([6]) initiatedthe problems imposed on submanifolds of Euclidean space of arbitrary codimensionrelated to Nashs embedding theorem. Many geometers have been working on relatedproblems and applications since the late 1990. He began with the notion of delta-invariant ( n 1 ;:::;n k ) and sets up the maximal principle with it and the squaredmean curvature to de ne the ideal immersion which is used to characterize 1-typeimmersions which characterize minimal submanifolds in Euclidean space or a spaceform. Furthermore, this contributes to giving obstruction theorems for minimalimmersions in Euclidean space and Lagrangian immersions in complex Euclideanspace.Let