  Austere submanifolds of Euclidean space were introduced in 1982 by Harvey and
Lawson in their foundational work on calibrated geometries. In general, the
austerity condition is much stronger than minimality since it express that the
nonzero eigenvalues of the shape operator of the submanifold appear in opposite
pairs for any normal vector at any point. Thereafter, the challenging task of
finding non-trivial explicit examples, other than minimal immersions of Kaehler
manifolds, only turned out submanifolds of rank two, and these are of limited
interest in the sense that in this special situation austerity is equivalent to
minimality. In this paper, we present the first explicitly given family of
austere non-Kaehler submanifolds of higher rank, and these are produced from
holomorphic data by means of a Weierstrass type parametrization.

Differential Geometry