In this paper, we first investigate the Kenmotsu statistical structures built on a space form and determine some special under two curvature conditions. Secondly, show that if holomorphic sectional of hypersurface orthogonal to structure vector in manifold is constant, then $\phi-$sectional ambient must be constant $-1$, $0$. addition, non-trivial examples are given illustrate results paper.

In the present paper we obtained 2 identities, which are satisfied by Riemann curvature tensor of generalized Kenmotsu manifolds. There was an analytic expression for third structure or f -holomorphic sectional GK -manifold. We separated classes manifolds and collected their local characterization.

in this paper, the lorentzian version of beltrami-euler formula is investigated in 1n . initially,the first fundamental form and the metric coefficients of generalized timelike ruled surface are calculated and by the help of the christoffel symbols, riemann-christoffel curvatures are obtained. thus, the curvatures of spacelike and timelike tangential sections of generalized timelike ruled surf...

Kodaira embedding theorem provides an effective characterization of projectivity a Kahler manifold in terms the second cohomology. Recently X. Yang [21] proved that any compact with positive holomorphic sectional curvature must be projective. This gives metric criterion its curvature. In this note, we prove 2nd scalar (which is average over 2-dimensional subspaces tangent space) view generic 2-...

We study the asymptotic behavior of the Kähler-Ricci flow on Kähler manifolds of nonnegative holomorphic bisectional curvature. Using these results we prove that a complete noncompact Kähler manifold with nonnegative bounded holomorphic bisectional curvature and maximal volume growth is biholomorphic to complex Euclidean space C . We also show that the volume growth condition can be removed if ...

Let $(g, X)$ be a K\"ahler-Ricci soliton on complex manifold $M$. We prove that if the K\"ahler $(M, g)$ can immersed into definite or indefinite space form of constant holomorphic sectional curvature $2c$, then $g$ is Einstein. Moreover, its Einstein rational multiple $c$.

This article aims to investigate the curvature operator of second kind on Kähler manifolds. The first result states that an m-dimensional manifold with $$\frac{3}{2}(m^2-1)$$ -nonnegative (respectively, -nonpositive) must have constant nonnegative nonpositive) holomorphic sectional curvature. asserts a closed $$\left( \frac{3m^3-m+2}{2m}\right) $$ -positive has positive orthogonal bisectional c...