arXiv research

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, hyper-pseudo-Hermitian curvature model, or hyper-para-Hermitian curvature model can be realized by a manifold with co…

Study scalar curvatures in almost Hermitian geometry and derive inequalities and characterization results.

The study explores metrics with constant curvature on compact manifolds.

Paper explores prescribing Chern scalar curvatures on noncompact Hermitian manifolds.

Lower bound for L^2-norm of Hermitian scalar curvature derived from Futaki invariant.

The paper explores Kähler-like metrics on generalized flag manifolds.

The paper classifies flag manifolds with specific isotropy components and finds conditions for Kähler-like scalar curvature.

Paper investigates prescribing Chern scalar curvatures on specific manifolds.

Unified flow approach to curvature problem on specific manifolds.

The paper explores constant holomorphic d-scalar curvature on specific manifolds.

Study curvatures on compact pseudo-Hermitian manifolds using special methods.

We show that a Hermitian algebraic curvature model satisfies the Gray identity if and only if it is geometrically realizable by a Hermitian manifold. Furthermore, such a curvature model can in fact be realized by a Hermitian manifold of constant scalar curvature and constant *-scalar curvature which satisfies the Kaehl…

The paper constructs metrics on Hirzebruch surfaces and ruled surfaces.

Study local properties of Chern-scalar curvature through linearization stability.

We show that a para-Hermitian algebraic curvature model satisfies the para-Gray identity if and only if it is geometrically realizable by a para-Hermitian manifold. This requires extending the Tricerri-Vanhecke curvature decomposition to the para-Hermitian setting. Additionally, the geometric realization can be chosen …

The study of scalar curvatures on almost Hermitian manifolds and existence of conformally constant Chern scalar curvature metrics.

Paper solves Gauduchon scalar curvature problem on almost Hermitian manifolds.

A new flow of Hermitian metrics reduces to a scalar equation and preserves special structures.

For a Kahler metric, the Riemannian scalar curvature is equal to twice the Chern scalar curvature. The question we address here is whether this equivalence can hold for a non-Kahler Hermitian metric. For such metrics, if they exist, the Chern scalar curvature would have the same geometric meaning as the Riemannian sc…

The orthogonal decomposition of the Webster curvature provides us a way to characterize some canonical metrics on a pseudo-Hermitian manifold. We derive some subelliptic differential inequalities from the Weitzenböck formulas for the traceless pseudo-Hermitian Ricci tensor and the Chern-Moser tensor of Sasakian manifol…

In this article we show that any finite cover of the moduli space of closed Riemann surfaces of $g$ genus with $g\geq 2$ does not admit any complete finite-volume Hermitian metric of non-negative scalar curvature. Moreover, we also show that the total mass of the scalar curvature of any almost Hermitian metric, which i…

The paper explores curvature constraints on Kodaira dimension for specific almost Hermitian manifolds.

Study Bismut connection curvatures and solve Yamabe and Calabi-Yau problems.

Study on prescribing curvature on specific manifolds with negative Gauduchon degree.

Three problems in Hermitian geometry for canonical metrics.

Study on complex manifolds introduces a new deformation of the Yamabe problem.

Compact Riemann surfaces have specific curvature metrics based on genus and symmetric product.

The paper proves estimates for Hermitian metrics and shows curvature blow-up on complex manifolds.

The paper proves conditions for positive scalar curvature on complex manifolds.

The paper solves a problem related to curvature in complex geometry.

This paper generalizes a rigidity result of complex hyperbolic spaces by M. Herzlich. We prove that an almost Hermitian spin manifold $(M,g)$ of real dimension $4n+2$ which is strongly asymptotic to $\hyp{\C}^{2n+1}$ and satisfies a certain scalar curvature bound must be isometric to the complex hyperbolic space. The f…

Survey on metrics on non-Kähler complex manifolds.

We show that an almost Hermitian manifold $(M,g)$ of real dimension $4n$ which is strongly asymptotic to $\mathbb{C}H^{2n}$ and satisfies a certain scalar curvature bound must be isometric to the complex hyperbolic space. Assuming Kähler instead of almost Hermitian this gives the already known rigidity result by H. Bou…

Deform quantization recovers scalar curvature in complex structures.

Flow smooths Chern-Ricci-flat metrics on Hermitian manifolds.

Study on Hermitian metrics and curvature properties of complex manifolds.

The Chern sectional curvature of a Hermitian manifold is derived and related to Kähler metrics.

The study finds metrics with constant scalar curvature on complex manifolds.

Study on special Hermitian metrics on cohomogeneity one manifolds.

In this paper, we introduce the first Aeppli-Chern class for complex manifolds and show that the $(1,1)$- component of the curvature $2$-form of the Levi-Civita connection on the anti-canonical line bundle represents this class. We systematically investigate the relationship between a variety of Ricci curvatures on Her…

On a 4-dimensional compact symplectic manifold, we consider a smooth family of compatible almost-complex structures such that at time zero the induced metric is Hermite-Einstein almost-Kähler metric with zero or negative Hermitian scalar curvature. We prove, under certain hypothesis, the existence of a smooth family of…

On a Kahler manifold there is a clear connection between the complex geometry and underlying Riemannian geometry. In some ways, this can be used to characterize the Kahler condition. While such a link is not so obvious in the non-Kahler setting, one can seek to understand extensions of these characterizations to genera…

Various curvature conditions are studied on metrics admitting a symmetry group. We begin by examining a method of diagonalizing cohomogeneity-one Einstein manifolds and determine when this method can and cannot be used. Examples, including the well-known Stenzel metrics, are discussed. Next, we present a simplification…

The paper proves complex geometry results for manifolds of the form X × R², answering a 1994 conjecture.

The paper proves the Hermitian Curvature Flow preserves various curvature conditions.

The paper proves the existence of metrics with constant curvature on smoothings of orbifolds with $A_1$ singularities.

In this paper we study sectional curvature of invariant hyper-Hermitian metrics on simply connected 4-dimensional real Lie groups admitting invariant hypercomplex structure. We give the Levi-Civita connections and explicit formulas for computing sectional curvatures of these metrics and show that all these spaces have …

The paper extends Gray's result to quaternion-Kähler manifolds.