In this paper, we prove that if every totally real bisectional curvature of an n(≥ 3)-dimensional complete Kähler submanifold of a complex projective space of constant holomorphic sectional curvature c is greater than c 4(n2−1)n(2n− 1), then it is totally geodesic. Mathematics Subject Classifications: 53C50, 53C55, 53C56.

This paper constructs a class of complete Kähler metrics of positive holomorphic sectional curvature on C and finds that the constructed metrics satisfy the following properties: As the geodesic distance ρ → ∞, the volume of geodesic balls grows like O(ρ 2(β+1)n β+2 ) and the Riemannian scalar curvature decays like O(ρ − 2(β+1) β+2 ), where β ≥ 0.

Let M = X×Y be the product of two complex manifolds of positive dimensions. In this paper, we prove that there is no complete Kähler metric g on M such that: either (i) the holomorphic bisectional curvature of g is bounded by a negative constant and the Ricci curvature is bounded below by −C(1+r) where r is the distance from a fixed point; or (ii) g has nonpositive sectional curvature and the h...

In this paper, we proved that a compact Sasakian manifold [Formula: see text] with negative transverse holomorphic sectional curvature must have structure Ricci curvature. Similarly, nonpositive curvature, then the first basic Chern class is nef and Miyaoka–Yau-type inequality. When quasi-negative, obtain number

The notion of holomorphic bisectional curvature for a complex Finsler space (M, F ) is defined with respect to the Chern complex linear connection on the pull-back tangent bundle. By means of holomorphic curvature and holomorphic flag curvature of a complex Finsler space, a special approach is emloyed to obtain the characterizations of the holomorphic bisectional curvature. For the class of gen...

Cirelli, Manià and Pizzocchero generalized quantum mechanics by Kähler geometry. Furthermore they proved that any unital C-algebra is represented as a function algebra on the set of pure states with a noncommutative ∗-product as an application. The ordinary quantum mechanics is regarded as a dynamical system of the projective Hilbert space P(H) of a Hilbert space H. The space P(H) is an infinit...