  Let $M$ be a submanifold of a Riemannian manifold $(N,g)$. $M$ induces a
subbundle $O(M,N)$ of adapted frames over $M$ of the bundle of orthonormal
frames $O(N)$. Riemannian metric $g$ induces natural metric on $O(N)$. We study
the geometry of a submanifold $O(M,N)$ in $O(N)$. We characterize the
horizontal distribution of $O(M,N)$ and state its correspondence with the
horizontal lift in $O(N)$ induced by the Levi--Civita connection on $N$.
  In the case of extrinsic geometry, we show that minimality is equivalent to
harmonicity of the Gauss map of the submanifold $M$ with deformed Riemannian
metric. In the case of intrinsic geometry we compute the curvatures.
