Exceptional minimal surfaces with the Ricci condition

On minimal surfaces with the Ricci condition in space forms

“…Next we discuss exceptional minimal surfaces in X N (c) whose induced metrics satisfy the Ricci condition with respect to c. Remark 3. (i) There are flat exceptional minimal surfaces lying fully in X 2n+l (c), where c > 0 (see [9]).…”

“…(ii) There are non-flat exceptional minimal surfaces lying fully in X 4m+3 (c) whose induced metrics satisfy the Ricci condition with respect to c, where c > 0 (see [9]).…”

“…[9]). Let f : M -* X N (c) be an exceptional minimal immersion of a 1-dimensional manifold M into X N (c) where c > 0.…”

Rigidity of superconformal minimal surfaces lying fully in odd-dimensional unit spheres

“…Superconformal minimal surfaces lying fully in S 2 ™' 1 just correspond to exceptional minimal surfaces lying fully in S 2 " 1 ' 1 in the sense of Johnson [6] (cf. [8] and [9]).…”

Minimal surfaces with the Ricci condition in 4-dimensional space forms

“…In [13], with some global assumptions, Naka (= Miyaoka) obtained some results in the case where c > 0. In [ 14] we discussed exceptional minimal surfaces in XN(c) which satisfy the Ricci condition with respect to c.…”