arXiv research

The study characterizes real flag manifolds with invariant generalized almost complex structures.

The paper proves smoothness of weakly biharmonic almost complex structures in dimension four.

Study transverse Dolbeault cohomology for almost complex structures.

Study integrability of generalized almost complex structures on S^6.

Study on biharmonic almost complex structures on compact manifolds.

Study of complex and Hermitian structures on specific Lie groups.

Study shows a copy of 7D real projective space in the space of almost complex structures on 6-sphere.

Harmonic almost complex structures on specific Lie groups and solvmanifolds identified.

Study shows almost complex structures with certain tensor properties are prevalent.

In this paper we present some approaches to classification of almost complex structures and to construction of local or formal pseudoholomorphic mapping from one almost complex manifold to another. The corresponding criteria are given in terms of Nijenhuis tensors and their generalizations. We deal with the prolongatio…

No almost complex structures on the six-sphere satisfy certain commutation conditions.

This article is mostly a writeup of two talks, the first given in the Besse Seminar at the Ecole Polytechnique in 1998 and the second given at the 2000 International Congress on Differential Geometry in memory of Alfred Gray in Bilbao, Spain. It begins with a discussion of basic geometry of almost complex 6-manifolds. …

Study on invariant almost complex structures on real flag manifolds.

The paper finds a criterion for generating commuting pairs of structures.

Study integrability of specific geometric structures on odd Courant algebroids.

Generically an almost complex structure has no symmetries at all, but there exist symmetric structures. In this paper we describe how to guarantee that the pseudogroup of local symmetries is small (finite-dimensional). It will be indicated that a large symmetry pseudogroup (infinite-dimensional) is a signature of some …

The paper studies lifts of complex structures on a manifold.

The paper proves conditions for almost complex manifolds to admit almost complex structures through connected sums.

Positivity of intersections in 4-manifolds leads to taming symplectic structures.

The paper classifies invariant structures on complex almost Abelian groups.

We provide a general criteria for the integrability of the almost para-quaternionic structure of an almost para-quaternionic manifold (M,P) of dimension bigger or equal to eight, in terms of the integrability of two or three sections of the defining rank three vector bundle P. We relate it with the integrability of the…

Study on Kodaira dimension of SU(m)-structures on almost complex manifolds.

Study Hodge-de Rham numbers for almost complex 4-manifolds, extending properties from complex surfaces.

Odd m-fold connected sums of complex projective spaces admit almost complex structures.

Study of complex structures on product twistor spaces for 4D manifolds.

The paper connects complex contact structures to specific types of almost contact 3-structures.

Almost complex structures found on many homotopy complex projective spaces.

Expanding on previous work, this note generalizes geometric structures results.

Based on recent work of T. Draghici, T.-J. Li and W. Zhang, we further investigate properties of the dimension h_J of the J-anti-invariant cohomology subgroup H_J of a closed almost Hermitian 4-manifold (M, g, J, F) using metric compatible and symplectic 2-form compatible almost complex structures. We prove that h_J = …

To give an almost quaternionic structure on a 4n-manifold $M$ is equivalent to give its bundle of twistors $Z(Q)\longrightarrow M$. When $Q$ is invariant under a torsion free connection, $Z(Q)$ can be provided with an almost complex structure $\mathbb J$. In the case $n = 1$ Atiyah, Hitchin and Singer have related…

We define a generalized almost para-Hermitian structure to be a commuting pair $(\mathcal{F},\mathcal{J})$ of a generalized almost para-complex structure and a generalized almost complex structure with an adequate non-degeneracy condition. If the two structures are integrable the pair is called a generalized para-Kähle…

Conditions for hypersurfaces of generalized Kähler manifolds to have specific structures are established.

The paper studies almost complex structures on ACH Einstein manifolds and finds deformation results.

Study on Kodaira dimension of specific solvmanifolds without complex structures.

Study pseudo-Kähler structures on almost abelian solvmanifolds.

Study Kodaira dimensions on almost complex manifolds, proving integrability and structural descriptions.

Twilled L(ie-)R(inehart)-algebras generalize, in the Lie-Rinehart context, complex structures on smooth manifolds. An almost complex manifold determines an "almost twilled pre-LR algebra", which is a true twilled LR-algebra iff the almost complex structure is integrable. We characterize twilled LR structures in terms o…

Study on almost complex structures with maximal Nijenhuis tensor rank and cohomological properties.

The paper explores families of almost complex structures and transverse (p,p)-forms.

Overview of algebraic geometry for almost complex manifolds.

Study functionals on almost complex structures for Yau's Challenge.

In 2003, S.-s. Chern began a study of almost-complex structures on the 6-sphere, with the idea of exploiting the special properties of its well-known almost-complex structure invariant under the exceptional group $G_2$. While he did not solve the (currently still open) problem of determining whether there exists an int…

Solves a generalized Monge-Ampère equation on Kähler surfaces, proving a conjecture.

A conformal change of $TM\oplus T^*M$ is a morphism of the form $(X,α)\mapsto(X,e^τα)$ $(X\in TM,α\in T^*M,τ\in C^\infty(M))$. We characterize the generalized almost complex and almost Hermitian structures that are locally conformal to integrable and to generalized Kähler structures, respectively, and give examples of …

Improved optimal regularity for harmonic almost complex structures.

We study a special type of almost complex structures, called pure and full and introduced by T.J. Li and W. Zhang, in relation to symplectic structures and Hard Lefschetz condition. We provide sufficient conditions to the existence of the above type of almost complex structures on compact quotients of Lie groups by dis…

An \emph{$ω$-admissible almost complex structure} on a $2n$-dimensional symplectic manifold $(M,ω)$ is a $ω$-calibrated almost complex structure $J$ admitting a nowhere vanishing $\bar{\partial}_J$-closed $(n,0)$-form $ψ$. After giving some examples we consider the moduli space of admissible almost complex structures a…

For a compact almost complex 4-manifold $(M,J)$, we study the subgroups $H^{\pm}_J$ of $H^2(M, \mathbb{R})$ consisting of cohomology classes representable by $J$-invariant, respectively, $J$-anti-invariant 2-forms. If $b^+ =1$, we show that for generic almost complex structures on $M$, the subgroup $H^-_J$ is trivial. …