Negative vector bundle
A holomorphic vector bundle (cf. also Vector bundle, analytic) over a complex space
that possesses a Hermitian metric
such that the function
on
is strictly pseudo-convex outside the zero section (this is denoted by
). The vector bundle
is negative if and only if the dual vector bundle
(see Positive vector bundle). If
is a manifold, then the condition of being negative can be expressed in terms of the curvature of the metric
. Any subbundle of a negative vector bundle is negative. A vector bundle
over a complex manifold is said to be negative in the sense of Nakano if
is positive in the sense of Nakano. A holomorphic vector bundle
over a compact complex space
is said to be weakly negative if its zero section possesses a strictly pseudo-convex neighbourhood in
, i.e. if
is weakly positive. Every negative vector bundle over
is weakly negative. Negative and weakly negative linear spaces over a space
are also defined in this way.
For references see Positive vector bundle.
Negative vector bundle. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Negative_vector_bundle&oldid=32814