Hermitian Lie algebroids over analytic spaces

We explore complex Riemannian geometry and Hermitian metrics on complex algebraic varieties and analytic spaces, respectively. In particular, we introduce Hermitian metrics on holomorphic Lie algebroids and examine the associated characteristic foliation with its canonically induced inner product. Furthermore, we study hypercohomologies related to the leaf space, leaves, and certain invariant subspaces arising from the characteristic foliation of a holomorphic Lie algebroid over a Hermitian manifold. Finally, we extends the concept of equivariant de Rham cohomology to the setting of Hermitian Lie algebroids.