  Motivated by the theory of isoparametric hypersurfaces, we study submanifolds
whose tubular hypersurfaces have some constant "higher order mean curvatures".
Here a $k$-th order mean curvature $Q_k$ ($k\geq1$) of a hypersurface $M^n$ is
defined as the $k$-th power sum of the principal curvatures, or equivalently,
of the shape operator. Many necessary restrictions involving principal
curvatures, higher order mean curvatures and Jacobi operators on such
submanifolds are obtained, which, among other things, generalize some classical
results in the theory of isoparametric hypersurfaces given by E. Cartan, K.
Nomizu, H. F. M{\"u}nzner, Q. M. Wang, \emph{etc.}. As an application, we
finally get a geometrical filtration for the focal varieties of isoparametric
functions on a complete Riemannian manifold.
