Austerity is a pointwise algebraic condition on the second fundamental form of an Euclidean
submanifold and requires that the nonzero principal curvatures in any normal direction occur …

A second order family of special Lagrangian submanifolds of C m is a family characterized
by the satisfaction of a set of pointwise conditions on the second fundamental form. For …

In general, not much is known about minimal submanifolds of Euclidean space of high
codimension. In [1], Anderson studies complete minimal submanifolds of Euclidean space …

This is the fifth in a series of papers constructing explicit examples of special Lagrangian
submanifolds in, giving both general theory and families of examples. Our results are related …

This is the third in a series of papers constructing explicit examples of special Lagrangian
submanifolds in C m. The previous paper (Math. Ann. 320 (2001), 757–797), defined the …

We extend the 'bundle constructions' of calibrated submanifolds, due to Harvey–Lawson in
the special Lagrangian case, and to Ionel–Karigiannis–Min-Oo in the cases of exceptional …

We study special Lagrangian submanifolds in the Calabi-Yau manifold $ T^* S^ n $ with the
Stenzel metric, as well as calibrated submanifolds in the $\text {G} _2 $-manifold $\Lambda …

0. Introduction. In [HL1], Harvey and Lawson provethat Re dz (dz dzl^^ dzn) is a calibration
on C R2n, where z (z1,..., zn) are the coordinates on C'. Let P be an n-dimensional oriented …

We prove that for n>1 one cannot immerse S^2n as a minimal Lagrangian manifold into a
hyperKähler manifold. More generally we show that any minimal Lagrangian immersion of …

The notion of calibrations and calibrated submanifolds originates from the seminal paper
[HL82] of Harvey and Lawson. Apart from the rich theory of calibrated submanifolds, the link …