Minimal submanifolds of a sphere with bounded second fundamental form
Author:
Hillel Gauchman
Journal:
Trans. Amer. Math. Soc. 298 (1986), 779-791
MSC:
Primary 53C42
DOI:
https://doi.org/10.1090/S0002-9947-1986-0860393-5
MathSciNet review:
860393
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Abstract | References | Similar Articles | Additional Information
Abstract: Let be the second fundamental form of an
-dimensional minimal submanifold
of a unit sphere
,
be the square of the length of
, and
for any unit vector
. Simons proved that if
on
, then either
, or
. Chern, do Carmo, and Kobayashi determined all minimal submanifolds satisfying
. In this paper the analogous results for
are obtained. It is proved that if
, then either
, or
. All minimal submanifolds satisfying
are determined. A stronger result is obtained if
is odd-dimensional.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1986-0860393-5
Article copyright:
© Copyright 1986
American Mathematical Society