A Preserved Geometric Property Along the Second Ricci Flow on Noncompact Almost Hermitian Manifolds

We show the short-time existence of the second Ricci flow on a complete noncompact almost Hermitian manifold, and prove that along the second Ricci flow, the nonpositivity of the first Chern–Ricci curvature can be preserved if the initial almost Hermitianmetric has non-positive bisectional curvature. If additionally the first Chern– Ricci curvature of the initial metric is negative at least at one point, then we show that the almost complex structure of a complete noncompact non-quasi-Kähler almost Hermitian manifold equipped with such a metric cannot be integrable.