Suppose that M is a complete Kähler manifold such its holomorphic sectional curvature bounded from below by constant and radial also below. N strongly pseudoconvex complex Finsler above negative constant. In this paper, we establish Schwarz lemma for mappings f into N. As applications, obtain Liouville type rigidity result N, as well theorem bimeromorphic compact manifold.

This paper determined the components of generalized curvature tensor for class Kenmotsu type and established mentioned is {\eta}-Einstein manifold when flat; converse holds true under suitable conditions. It also introduced notion {\Phi}-holomorphic sectional (G{\Phi}SH-) thus found necessary sufficient conditions to be constant G{\Phi}SH-curvature. In addition, {\Phi}-generalized semi-symmetri...

In this paper, we prove a general maximum principle for the time dependent Lichnerowicz heat equation on symmetric tensors coupled with the Ricci flow on complete Riemannian manifolds. As an application we construct complete manifolds with bounded nonnegative sectional curvature of dimension greater than or equal to four such that the Ricci flow does not preserve the nonnegativity of the sectio...

We apply the existence and special properties of Gauduchon metrics to give several applications. The first one is concerned with implications algebro-geometric nature under a Hermitian metric nonnegative holomorphic sectional curvature. second show non-existence sections on vector bundles certain conditions. third restriction $\partial\bar{\partial}$-closedness some real $(n-1,n-1)$-forms compa...

We examine the class of compact Hermitian manifolds with constant holomorphic sectional curvature. Such are conjectured to be K\"ahler (hence a complex space form) when is non-zero and Chern flat quotient Lie group) zero. The conjecture known in dimension two but open higher dimensions. In this paper, we establish partial solution three by proving that any threefold zero real bisectional curvat...

Abstract We show that the singularities of twisted Kähler–Einstein metric arising as longtime solution Kähler–Ricci flow or in collapsed limit Ricci-flat Kähler metrics are intimately related to holomorphic sectional curvature reference conical geometry. This provides an alternative proof second-order estimate obtained by Gross, Tosatti, and Zhang (2020, Preprint, arXiv:1911.07315) with explici...