Gap Theorems for Certain Submanifolds of Euclidean Spaces and Hyperbolic Space Forms

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