It is well known that \({\mathbb {C}}H^n\) has the structure of a solvable Lie group with left invariant metric constant holomorphic sectional curvature. In this paper we give full classification all possible Riemannian metrics on group. We prove each those negative scalar curvature, only one them being Einstein (up to isometry and scaling).

We prove that a smooth complex projective threefold with a Kähler metric of negative holomorphic sectional curvature has ample canonical line bundle. In dimensions greater than three, we prove that, under equal assumptions, the nef dimension of the canonical line bundle is maximal. With certain additional assumptions, ampleness is again obtained. The methods used come from both complex differen...

This paper discusses the Norden golden manifold having a constant sectional curvature. First, it is shown that if has real curvature, flat. For this reason, notions of holomorphic-like curvature and bisectional on are investigated, but seen these do not work manifold. shows need for new concept In direction, notion (Norden curvature) proposed, an example given, constant, tensor field expressed ...