I am assuming you are asking the question on a compact Kahler manifold. You can find argument in Mok's paper for the part of non-negativity of holomorphic bisectional curvature (HSBC) is preserved under Kahler Ricci flow.(http://projecteuclid.org/download/pdf_1/euclid.jdg/1214441778) Roughly speaking, we need to compute the evolution equation of HSBC, then we will get a quadratic term involving curvature besides the heat operator. If the quadratic term satisfies "null vector condition", then the maximal principle will get us the result.

I am assuming you are asking the question on a compact Kahler manifold. You can find argument in Mok's paper for the part of non-negativity of holomorphic bisectional curvature (HBSC) is preserved under Kahler Ricci flow.(http://projecteuclid.org/download/pdf_1/euclid.jdg/1214441778) Roughly speaking, we need to compute the evolution equation of HBSC, then we will get a quadratic term involving curvature besides the heat operator. If the quadratic term satisfies "null vector condition", then the maximal principle will get us the result.