Riv.Mat.Univ.Parma (6) 2 (1999)

M. D'APRILE and V. MARINO

Sulla geometria di varietà ortogonali di codimensione alta nello spazio euclideo

Pages: 103-118
Abstract: We generalize a paper of M.A. Cheshkova to the case of a diffeomorphism $f: M \to \overline{M}$, $M , \overline{M}$ being $n$-dimensional submanifold of $E^{2 n +q},$ such that for any $p\in M$ the first normal space $Nor^1 M_p$ coincides with the tangent space $\overline{M}_{f(p)}$ ($1$-orthogonal manifolds). We establish relations between the curvature tensors of $M$ and $\overline{M}$ and find a condition on the mean curvature field of $\overline{M}$ for $M$ to be minimal and a condition for $f$ to be an harmonic map.