Hermitian metric
From Exampleproblems
In mathematics, a Hermitian metric g on a vector space with an almost complex structure J is a metric such that
A Hermitian metric on an almost complex vector bundle E over a manifold M, is a section of the bundle E2* which is a Hermitian metric at each point of M.
An important special case is that of a Hermitian metric on the complexified tangent bundle 
of a complex manifold M. This is the hermitian analogue of a Riemannian metric. Every complex manifold admits such a hermitian metric.
