Abstract
In this paper we show that for a compact minimal hypersurface
M
of constant scalar curvature in the unit sphere
S
6
with the shape operator
A
satisfying
‖
A
‖
2
>
5
, there exists an eigenvalue
λ
>
10
of the Laplace operator of the hypersurface
M
such that
‖
A
‖
2
=
λ
−
5
. This gives the next discrete value of
‖
A
‖
2
greater than 0 and 5.