arXiv research

In this paper, by using the Bochner technique on almost Hermitian manifolds, we obtain a complex Hessian comparison for almost Hermitian manifolds generalizing the Laplacian comparison for almost Hermitian manifolds by Tossati, and reprove a diameter estimate for almost Hermitian manifolds by Gray. Moreover, we obtain …

Characterizes a class of almost Hermitian 4-manifolds using integral identities.

We introduce a new curvature flow which matches with the Ricci flow on metrics and preserves the almost Hermitian condition. This enables us to use Ricci flow to study almost Hermitian manifolds.

Surveying locally homogeneous almost-Hermitian spaces with formulas for curvature.

The Almost Hermitian Curvature flow was introduced by Streets and Tian in order to study almost hermitian structures, with a particular interest in symplectic structures. This flow is given by a diffusion-reaction equation. Hence it is natural to ask the following: which almost hermitian structures are dynamically stab…

Paper generalizes sub-slope definition and solves complex equations on compact manifolds.

The paper studies equations on almost Hermitian manifolds with estimates and existence results.

Holomorphic maps are a special case of Hermitian pluriharmonic maps between almost Hermitian manifolds.

Paper establishes estimates for solutions on compact manifolds.

The Schur's theorem of antiholomorphic type is proved for arbitrary almost Hermitian manifolds, namely: If a connected almost Hermitian manifold of dimension greater or equal to 6 is of pointwise constant antiholomorphic sectional curvature, then this curvature is a global constant.

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

Study on slant submanifolds with new conditions and transitivity.

The fundamental 2-form of an invariant almost Hermitian structure on a 6-dimensional Lie group is described in terms of an action by SO(4)xU(1) on complex projective 3-space. This leads to a combinatorial description of the classes of almost Hermitian structures on the Iwasawa and other nilmanifolds.

Compactify complex hyperbolic almost Hermitian manifolds.

Paper proves solutions for deformed Hermitian-Yang-Mills equation on almost Hermitian manifolds.

In this paper, by introducing a notion of local quasi holomorphic frame, we obtain a curvature formula for almost Hermitian manifolds which is similar to that of Hermitian manifolds. Moreover, as applications of the curvature formula, we extend a result of H.S. Wu and a result of F. Zheng to almost Hermitian manifolds.

The study classifies natural almost Hermitian structures on specific Lie groups.

Criterions for constancy of the holomorphic sectional curvature and the antiholomorphic sectional curvature are proved for almost Hermitian manifolds. It is shown, that an almost Hermitian manifold satisfying the axiom of antiholomorphic planes or the axiom of antiholomorphic spheres is a real or a complex space form.

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

New operators generalize Michelsohn's on almost Hermitian manifolds.

Study of almost Yamabe solitons on Kaehler submersions.

It is proved, that if an almost Hermitian manifold satisfies the axiom of coholomorphic spheres, it is conformal flat.

The paper studies twisted almost Hermitian structures on the 6-sphere.

The paper studies quarter-symmetric connections on Hermitian and Kähler manifolds.

Extends three circle theorem to almost Hermitian manifolds.

In this paper, we systematically compute the Bianchi identities for the canonical connection on an almost Hermitian manifold. Moreover, we also compute the curvature tensor of the Levi-Civita connection on almost Hermitian manifolds in terms of curvature and torsion of the canonical connection. As applications of the c…

We prove the following results: An almost Hermitian manifold of indefinite metric is of pointwise constant holomorphic sectional curvature if the holomorphic sectional curvature is bounded from above and from below. If the antiholomorphic sectional curvature is bounded either from above or from below, then the manifold…

Study computes invariants on six-dimensional solvmanifolds, providing symplectic structure obstructions.

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

Paper solves complex Monge-Ampère equation on almost Hermitian manifolds.

Study shows that dimension of Dolbeault harmonic forms is not always equal to B- on certain 4-manifolds.

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

Study on harmonic forms on almost Hermitian 4-manifolds, calculating dimensions and invariants.

We study the curvature of almost Hermitian manifolds and their special analogues via intrinsic torsion and representation theory. By deriving different forumlae for the skew-symmetric part of the star-Ricci curvature, we find that some of these contributions are dependent on the approach used, and for the almost Hermit…

Study pseudoholomorphic maps using canonical connection.

We prove the long time existence and uniqueness of solutions to the parabolic Monge-Ampère equation on compact almost Hermitian manifolds. We also show that the normalization of solution converges to a smooth function in $C^{\infty}$ topology as $t\rightarrow\infty$. Up to scaling, the limit function is a solution of t…

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…

We introduce holomorphic Riemannian maps between almost Hermitian manifolds as a generalization of holomorphic submanifolds and holomorphic submersions, give examples and obtain a geometric characterization of harmonic holomorphic Riemannian maps from almost Hermitian manifolds to Kaehler manifolds.

We give a condition for an almost constant-type manifold to be a constant-type manifold, and holomorphic and $R$-invariant submanifolds of almost Hermitian manifolds are studied. Generalizations of some results in [5] are given.

The study examines harmonic forms on almost Hermitian manifolds and complex surfaces.

The paper classifies natural almost Hermitian structures on Lie groups with minimal conformal leaves.

It is proved that if an almost Hermitian manifold of dimension greater than 4 has vanishing (classical) Bochner curvature tensor and is not Kaehlerian at a point, then it is flat in a neighbourhood of this point.

Study of Hermitian and Gauduchon connections on Lie groups with almost Hermitian structures.

We study almost Hermitian structures admitting a Hermitian connexion with totally skew-symmetric torsion or equivalently, those almost Hermitian structures with totally skew-symmetric Nijenhuis tensor. We investigate up to what extent the Nijenhuis tensor fails to be parallel with respect to the characteristic connexio…

The axiom of θ-holomorphic 2-planes is introduced. It is proved, that if an almost Hermitian manifold satisfies this axiom for a fixed θ, 0< θ< π/2, then it is a real space form.

Study geometric inequalities for CR-submanifolds using curvature invariants.

Paper solves Gauduchon scalar curvature problem on almost Hermitian manifolds.

We study curvature properties of four-dimensional almost Hermitian manifolds with vanishing Bochner curvature tensor as defined by Tricerri and Vanhecke. We give local structure theorems for such Kaehler manifolds, and find out several examples related to the theorems.