Let
M
be an orientable hypersurface of an
-dimensional Einstein manifold
As for hypersurfaces of a real space
form, one is interested in obtaining conditions under which the hypersurface is
a real space form. In this paper, we are interested in finding conditions under
which
the
hypersurface
M
of
the
Einstein
manifold
is
an
Einstein
manifold. Let
N be the unit normal vector field of the hypersurface
M.
We say that the Einstein manifold
has constant mixed sectional
curvature with respect to the hypersurface
M if the sectional curvatures of
of the plane sections containing the
unit normal vector field
N are
constant.
In this paper, we
show that a compact orientable positively curved hypersurface
M of an
-dimensional Einstein manifold
of constant mixed sectional
curvature
c satisfying the inequality
is an Einstein
manifold, where
is the gradient of the mean
curvature a, A
is the shape operator and
is the Ricci curvature of the
hypersurface M (cf. Main Theorem). 
Home
