  Given a vector field $X$ in a Riemannian manifold, a hypersurface is said to
have a canonical principal direction relative to $X$ if the projection of $X$
onto the tangent space of the hypersurface gives a principal direction. We give
different ways for building these hypersurfaces, as well as a number of useful
characterizations. In particular, we relate them with transnormal functions and
eikonal equations. With the further condition of having constant mean curvature
(CMC) we obtain a characterization of the canonical principal direction
surfaces in Euclidean space as Delaunay surfaces. We also prove that CMC
constant angle hypersurfaces in a product $\mathbb{R}\times N$ are either
totally geodesic or cylinders.
