Highly Influenced

@inproceedings{KASUE2007GapTF, title={Gap Theorems for Certain Submanifolds of Euclidean Spaces and Hyperbolic Space Forms}, author={ATSUSHI KASUE and Kunio Sugahara}, year={2007} }

- Published 2007

Simons [18] studied minimal submanifolds of spheres and showed, among other things, that a compact minimal submanifold M of the unit w-sphere must be totally geodesic if the square length of the second fundamental form is less than nl(2—p~) (p=codimM) (cf. [13] for the equality discussion). Later, Ogiue [16] and Tanno [20] considered complex submanifolds in the complex projective space and obtained similar results to the Simons' theorem (cf. [17] for other related topics and the references). On… CONTINUE READING