In this paper, the Laplacian on the holomorphic tangent bundle $T^{1,0}M$ of a complex manifold $M$ endowed with a strongly pseudoconvex complex Finsler metric is defined and its explicit expression is obtained by using the Chern Finsler connection associated to $(M,F)$. Utilizing the initiated "Bochner technique", a vanishing theorem for vector fields on the holomorphic tangent bundle $T^{1,0}M$ is obtained.

Professor Qiu is currently the Professor of Mathematics and the Associate Dean of School of Mathematical Sciences in Xiamen University, where he received his Ph. D. degree. He is interested in Several Complex Variables, Complex Finsler Geometry and Clifford Analysis. His publications include, The singular integral equations on a closed piecewise smooth manifold in Cⁿ, Poincare-Bertrand formula of a singular integral on a closed piecewise smooth manifold, A new formula without boundary integrals on a Stein manifold, Weighted homotopy formulas on a local q-convex wedge in a complex manifold etc.