 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 EuclideanspaceLet

Isotropic Submanifolds of Real Space Forms

In the present paper, screen isotropic leaves on lightlike hypersurfaces of a Lorentzian manifold are introduced and studied which are inspired by the definition of isotropic immersions in the Riemannian context. Some examples of such leaves are mentioned. Furthermore, some relations involving curvature invariants are obtained.

Screen isotropic leaves on lightlike hypersurfaces of a lorentzian manifold

We study the length of second fundamental form of submanifolds with nonnegative Ricci curvature in a Euclidean space and prove that submanifolds are totally geodesic if a function on the unit tangent bundle satisfies a certain inequality concerning with the mean curvature vector.

Seong-Soo Ahn

Papers

Submanifolds of Euclidean Space with Non-Negative Ricci Curvature