Abstract
In this paper we study the role of constant vector fields on a Euclidean space
R
n
+
p
in shaping the geometry of its compact submanifolds. For an
n
-dimensional compact submanifold
M
of the Euclidean space
R
n
+
p
with mean curvature vector field
H
and a constant vector field
on
R
n
+
p
, the smooth function
is used to obtain a characterization of sphere among compact submanifolds of positive Ricci curvature (cf. main Theorem).