相关论文: Almost complex surfaces in the nearly K\"ahler $S^…

We study almost complex surfaces in the nearly K\"ahler $S^3\times S^3$. We show that there is a local correspondence between almost complex surfaces and solutions of the H-surface equation introduced by Wente. We find a global holomorphic…

We give a detailed description of the nearly K\"ahler $\frac{\mathrm{SL}(3,\mathbb R)}{\mathbb R\times \mathrm{SO}(2)}$, which is one of the pseudo-Riemannian counterparts of the flag manifold $F(\mathbb{C}^3)$. The main result is the…

In this paper, extending our previous joint work (Hu et al., Math Nachr 291:343--373, 2018), we initiate the study of Hopf hypersurfaces in the homogeneous NK (nearly K\"ahler) manifold $\mathbf{S}^3\times\mathbf{S}^3$. First, we show that…

The space $SL(2,\mathbb{R})\times SL(2,\mathbb{R})$ admits a natural homogeneous pseudo-Riemannian nearly Kaehler structure. We investigate almost complex surfaces in this space. In particular we obtain a complete classification of the…

Totally real surfaces in the nearly K\"ahler $\mathbb{C}P^3$ are investigated and are completely classified under various additional assumptions, resulting in multiple new examples. Among others, the classification includes totally real…

In this paper, we study degenerate almost complex surfaces in the semi-Riemannian nearly K\"ahler $\mathrm{SL}_2\mathbb{R}\times \mathrm{SL}_2\mathbb{R}$. The geometry of these surfaces depends on the almost product structure of the ambient…

A nearly K\"ahler manifold is an almost Hermitian manifold with the weakened K\"ahler condition, that is, instead of being zero, the covariant derivative of the almost complex structure is skew-symmetric. We give the explicit…

Hypersurfaces are studied and classified under multiple additional assumptions in any Riemannian homogeneous space $(\mathbb{C}P^3, g_a)$, including nearly K\"ahler $\mathbb{C}P^3$. Notably, all extrinsically homogeneous hypersurfaces are…

In the context of six-dimensional homogeneous nearly K\"ahler manifolds, we prove that $\mathbb S^6$ is the only ambient space admitting constant sectional curvature hypersurfaces. In order to do so, we prove first that in $\mathbb…

We define two transforms between non-conformal harmonic maps from a surface into the 3-sphere. With these transforms one can construct, from one such harmonic map, a sequence of harmonic maps. We show that there is a correspondence between…

A well known consequence of the Wirtinger inequality is that in a Kaehler surface a holomorphic curve is an area minimizer in its homology class. In light of this result it is natural, given a Kaehler surface, to investigate the relation…

The aim of these notes is to acquaint the reader with important objects in complex algebraic geometry: K3 surfaces and their higher-dimensional analogs, hyperk\"ahler manifolds. These manifolds are interesting from several points of view:…

Each hypersurface of a nearly K\"ahler manifold is naturally equipped with two tensor fields of $(1,1)$-type, namely the shape operator $A$ and the induced almost contact structure $\phi$. In this paper, we show that, in the homogeneous NK…

We deal with minimal surfaces in spheres that are locally isometric to a pseudoholomorphic curve in a totally geodesic $\mathbb{S}^{5}$ in the nearly K{\"a}hler sphere $\mathbb{S}^6$. Being locally isometric to a pseudoholomorphic curve in…

For K\"ahler K3 surfaces we consider Kulikov models of type III tamed by a symplectic form. Our main result shows that the generic smooth fiber admits an almost toric fibration over the intersection complex, which inherits a natural nodal…

We study the $\rm{SU}(3)$-structure induced on an oriented hypersurface of a 7-dimensional manifold with a nearly parallel $\rm{G}_2$-structure. We call such $\rm{SU}(3)$-structures nearly half-flat. We characterise the left invariant…

We consider a quadratic form defined on the surfaces with parallel mean curvature vector of an any dimensional complex space form and prove that its $(2,0)$-part is holomorphic. When the complex dimension of the ambient space is equal to…

We study the structure of $\mathfrak{M}_2$, the set of half-dimensional collapsing spaces of hyperk\"ahler metrics on K3 surfaces. We show that $\mathfrak{M}_2$ consists precisely of those underlying metric spaces of integral singular…

In a previous paper, the authors together with L. Vrancken initiated the study of $3$-dimensional CR submanifolds of the nearly K\" ahler homogeneous $\mathbb S^3\times \mathbb S^3$. As is shown by Butruille this is one of only four…

The aim of the paper is to investigate the rigidity and the deformability of pseudoholomorphic curves in the nearly K{\"a}hler sphere $\mathbb{S}^6,$ among minimal surfaces in spheres. Under various assumptions we describe the moduli space…