On Gauss-Bonnet And Poincare-Hopf Type Theorems For Complex Partial Derivative-Manifolds

We prove a Gauss-Bonnet and Poincare-Hopf type theorem for complex partial derivative-manifold (X) over tilde = X - D, where X is a complex compact manifold and D is a reduced divisor. We will consider the cases such that D has isolated singularities and also if D has a (not necessarily irreducible) decomposition D = D-1 boolean OR D-2 such that D-1, D-2 have isolated singularities and C = D-1 boolean AND D-2 is a codimension 2 variety with isolated singularities.