Related papers: Morse-type integrals on non-K\"ahler manifolds

Let $M_1$ and $M_2$ be two K\"ahler manifolds. We call $M_1$ and $M_2$ {\em relatives} if they share a non-trivial K\"ahler submanifold $S$, namely, if there exist two holomorphic and isometric immersions (K\"ahler immersions) $h_1: S\to…

A Hermitian-symplectic metric is a Hermitian metric whose K\"ahler form is given by the $(1,1)$-part of a closed $2$-form. Streets-Tian Conjecture states that a compact complex manifold admitting a Hermitian-symplectic metric must be…

We study a fully nonlinear equation of complex Monge-Ampere type on Hermitian manifolds. We establish the a priori estimates for solutions of the equation up to the second order derivatives with the help of a subsolution.

In a previous paper, under the assumption that the Riemannian metric is special, the author proved some results about the moduli spaces and CW structures arising from Morse theory. By virtue of topological equivalence, this paper extends…

Among other results, a compact almost K\"ahler manifold is proved to be K\"ahler if the Ricci tensor is semi-negative and its length coincides with that of the star Ricci tensor or if the Ricci tensor is semi-positive and its first order…

We use certain Morse functions to construct conformal metrics with negative sectional curvature on locally conformally flat manifolds with boundary. Moreover, without conformally flatness assumption, we also construct conformal metric of…

We show that a certain class of affine hyperplane arrangements are $K(\pi,1)$ by endowing their Falk complexes with an injective metric. This gives new examples of infinite $K(\pi,1)$ arrangements in dimension $n>2$.

There are studied Lie groups considered as almost hypercomplex Hermitian-Norden manifolds, which are integrable and have the lowest dimension four. It is established a correspondence of the derived Lie algebras of types of invariant…

Examples of Morse functions with integrable gradient flows on some classical Riemannian manifolds are considered. In particular, we show that a generic height function on the symmetric embeddings of classical Lie groups and certain…

Let $X$ be a normal compact K\"ahler variety, and $\mathcal{F}$ a coherent reflexive sheaf on $X$. We investigate the existence of admissible Hermitian metrics on $\mathcal{F}$. If moreover $\mathcal{F}$ is slope stable, we also study the…

By using analytic method, we prove that there exist rational curves on compact Hermitian manifolds with positive holomorphic bisectional curvature. It confirms a question of S.-T. Yau. It is well-known that Mori proved in \cite{Mori79} that…

We show that the classifying space of the flow category of a \emph{tame} Morse function on a smooth, closed manifold $M$ recovers the homotopy type of $M$, thereby addressing a claim in a preprint of Cohen--Jones--Segal. The tameness…

In this paper we are concerned with harmonic maps and minimal immersions defined on compact Riemannian manifolds and with values in homogenous strongly harmonic manifolds. We show some results on the Morse index by varying these maps along…

We prove that the integral Hodge conjecture holds for 1-cycles on irreducible holomorphic symplectic varieties of K3 type and of Generalized Kummer type. As an application, we give a new proof of the integral Hodge conjecture for cubic…

We study complex Monge-Ampere equations on Hermitian manifolds, extending classical existence results of Yau and Aubin in the Kahler case, and those of Caffarelli, Kohn, Nirenberg and Spruck for the Dirichlet problem in $C^n$. As an…

This article is concerned with Chern class and Chern number inequalities on polarized manifolds and nef vector bundles. For a polarized pair $(M,L)$ with $L$ very ample, our first main result is a family of sharp Chern class inequalities.…

We study $n$-dimensional K\"ahler manifolds whose geodesic flows possess $n$ first integrals in involution that are fibrewise hermitian forms and simultaneously normalizable. Under some mild assumption, one can associate with such a…

Almost para-Hermitian manifold it is manifold equipped with almost para-complex structure and compatible pseudo-metric of neutral signature. It is considered a class of immersions of almost para-Hermitian manifolds into almost…

We give a classification of compact conformally Kahler Einstein-Weyl manifolds whose Ricci tensor is hermitian.

In this paper, we study the non-Hermitian Yang-Mills (NHYM for short) bundles over compact K\"ahler manifolds. We show that the existence of harmonic metrics is equivalent to the semisimplicity of NHYM bundles, which confirms the Conjecture…