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...

We show any Riemannian curvature model can be geometrically realized by a manifold with constant scalar curvature. We also show that any pseudo-Hermitian curvature model, para-Hermitian curvature model, hyperpseudo-Hermitian curvature model, or hyper-para-Hermitian curvature model can be realized by a manifold with constant scalar and ⋆-scalar curvature.

The object of this paper is to study $(epsilon)$-Lorentzian para-Sasakian manifolds. Some typical identities for the curvature tensor and the Ricci tensor of $(epsilon)$-Lorentzian para-Sasakian manifold are investigated. Further, we study globally $phi$-Ricci symmetric and weakly $phi$-Ricci symmetric $(epsilon)$-Lorentzian para-Sasakian manifolds and obtain interesting results.

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...

We study complete noncompact long time solutions (M, g(t)) to the Kähler-Ricci flow with uniformly bounded nonnegative holomorphic bisectional curvature. We will show that when the Ricci curvature is positive and uniformly pinched, i.e. Ri̄ ≥ cRgi̄ at (p, t) for all t for some c > 0, then there always exists a local gradient Kähler-Ricci soliton limit around p after possibly rescaling g(t) alon...

In this paper, we first establish several theorems about the estimation of distance function on real and strongly convex complex Finsler manifolds then obtain a Schwarz lemma from weakly K\"ahler-Finsler manifold into pseudoconvex manifold. As applications, prove that holomorphic mapping is necessary constant under an extra condition. particular, Minkowski space such its sectional curvature bou...

A class of nearly Sasakian manifolds is considered in this paper. We discuss the geometric effects some symmetries on such and show, under a certain condition, that Ricci semi-symmetric subclass Einstein manifolds. prove Codazzi-type space form either manifold with constant ϕ-holomorphic sectional curvature H=1 or 5-dimensional proper H>1. also spectrum operator H2 generated by set simple ei...