On the Kobayashi metric for perturbations of the ball
The infinitesimal Kobayashi metric at 0 is studied for smooth \((C^ k,k \geq 6)\) perturbations of the ball in \(\mathbb{C}^ n\); the notion of a first- order hermitian flow is defined. A first-variation formula with an intuitive geometric interpretation is computed for the Kobayashi metric. This is used to derive integro-differential equations whose solutions are the first-order hermitian flows. If a flow is both first-order hermitian and first-order circular, the real normal component of its variation vector field is a linear combination of the real parts of type (1,1) quadratic polynomials.
scientific article; zbMATH DE number 549728