. For a complex manifold (M, J), an SKT (or pluriclosed) metric is a J-Hermitian metric g whose fundamental form omega := g(J, ) satisfies the condition partial derivative partial derivative (over bar)omega = 0. As such, an SKT metric can be regarded as a natural generalization of a Kahler metric. In this paper, the exceptional Lie group G(2)is equipped with a leftinvariant integrable almost complex structure J via the Samelson construction and a 7-parameter family of J-Hermitian metrics is constructed. From this 7-parameter family, the members which are SKT are calculated. The result is a 3-parameter family of left-invariant SKT metrics on G(2). As a special case, the aforementioned family of SKT metrics contains all bi-invariant metrics on G(2). In addition, this 3-parameter family of left-invariant SKT metrics is also invariant under the right action of a certain maximal torus T of G(2). Conversely, it is shown that if g is a left-invariant J-Hermitian metric on G(2)such that g is invariant under the right action of T and for which (g, J ) is SKT, then g must belong to this 3-parameter family of left-invariant SKT metrics.
We show that the second Jacobian ideal of a hypersurface can be decomposed such that a power of the Jacobian ideal becomes a factor. As an application of the decomposition, we present an elementary proof establishing that the second Nash blow-up algebra of a hypersurface singularity is a contact invariant.
