  In this paper we prove rigidity results for the sphere, the plane and the
right circular cylinder as the only self-shrinkers satisfying a new geometric
assumption, namely the union of all tangent affine submanifolds of a complete
self-shrinker omits a non-empty set of the Euclidean space. This assumption
lead us to a new class of submanifolds, different from those with polynomial
volume growth or the proper ones (which was proved to be equivalent by Cheng
and Zhou, see Proc. Amer. Math. Soc. 141 (2013), no. 2, 687-696). In fact, in
the last section, we present an example of a non proper surface whose tangent
planes omit the interior of a right circular cylinder, which proves that these
classes are distinct from each other.
