We characterize the q-pseudoconvexity for unramified Riemann domains over ℂⁿ, where 1≤q≤n, by the continuity property which holds for a class of maps whose projections to ℂⁿ are families of unidirectionally parameterized q-dimensional analytic balls written by polynomials of degree at most two.
Abe et al. (2019) studied this question.