  In this paper, we investigate the base complex manifold of an effectively
parameterized holomorphic family of stable Higgs bundles over a fixed compact
K\"{a}hler manifold. We first briefly recall Biswas-Schumacher's work on the
curvature formula of the Weil-Petersson metric on the base manifold, the
semipositivity of the holomorphic sectional curvature implies some geometric
properties of the base manifold. Then we calculate the curvature on the higher
direct image bundle over the base manifold, which recovers Biswas-Schumacher's
curvature formula. Finally, we construct a smooth and strongly pseudo-convex
complex Finsler metric for the base manifold, the corresponding holomorphic
sectional curvature is calculated explicitly.
