Related papers: Hartogs phenomenon and the problem of complex sphe…

The spaces of flattenings of a simplicial sphere played a key role in the study of existence and uniqueness of differentiable structures on a simplicial sphere. In this paper, we will establish that the spaces of flattenings of some…

We discuss the complex geometry of two complex five-dimensional K\"ahler manifolds which are homogeneous under the exceptional Lie group $G_2$. For one of these manifolds rigidity of the complex structure among all K\"ahlerian complex…

Explicit representations of complex structures on closed manifolds are valuable, but relatively rare in the literature. Using isoparametric theory, we construct complex structures on isoparametric hypersurfaces with $g=4, m=1$ in the unit…

We consider a complex Plateau problem for strongly pseudoconvex contours in non K\"ahler manifolds. A positive solution in the case of manifolds carrying a pluriclosed Hermitian metric forms is given. For the general case we propose a…

We identify R^7 as the pure imaginary part of octonions. Then the multiplication in octonions gives a natural almost complex structure for the unit 6-sphere. It is known that a cone over a surface M in S^6 is an associative submanifold of…

We study the six-dimensional solvmanifolds that admit complex structures of splitting type classifying the underlying solvable Lie algebras. In particular, many complex structures of this type exist on the Nakamura manifold $X$, and they…

A generalization of classical theorems on the existence of sections of real, complex and quaternionic Stiefel manifolds is proved.

We give a short proof for the Hartogs's extension theorem on (n-1)-complete complex spaces.

Integrable problem of three vorteces on a plane and sphere are considered. The classification of Poisson structures is carried out. We accomplish the bifurcational analysis using the variables introduced in previous part of the work.

We give a new construction of the outer automorphism of the symmetric group on six points. Our construction features a complex Hadamard matrix of order six containing third roots of unity and the algebra of split quaternions over the real…

Let $Z$ be a compact, connected $3$-dimensional complex manifold with vanishing first and second Betti numbers and non-vanishing Euler characteristic. We prove that there is no holomorphic mapping from $Z$ onto any $2$-dimensional complex…

We classify all integrable complex structures on 6-dimensional Lie algebras of the form $\mathfrak{g}\times\mathfrak{g}$.

We compute all complex structures on indecomposable 6-dimensional real Lie algebras and their equivalence classes. We also give for each of them a global holomorphic chart on the connected simply connected Lie group associated to the real…

We present a (possibly) new sphere eversion based on the contractibility* of a certain subset of the space of immersions of the circle in the plane. (*: by strong deformation retraction)

There is a rich theory of so-called (strict) nearly Kaehler manifolds, almost-Hermitian manifolds generalising the famous almost complex structure on the 6-sphere induced by octonionic multiplication. Nearly Kaehler 6-manifolds play a…

Applying our recent classification of negative-twisting tight contact structures on Seifert fibered spaces whose base orbifold is a sphere, we provide the complete list of all the Brieskorn spheres carrying at most two symplectically…

We produce a large class of hyperbolic homology 3-spheres admitting arbitrarily many distinct tight contact structures. We also produce a sub-class admitting arbitrarily many distinct tight contact structures within the same homotopy class…

We have identified some necessary conditions for the existence of rigid sphere designs. In particular, we have successfully resolved the conjecture proposed by [Ban87]; Given fixed positive integers t and d, we show that there exist only…

We show that the only rational homology spheres which can admit almost complex structures occur in dimensions two and six. Moreover, we provide infinitely many examples of six-dimensional rational homology spheres which admit almost complex…

We determine the homotopy types of the independence complexes of the $(n \times 6)$-square grid graphs. In fact, we show that these complexes are homotopy equivalent to wedges of spheres.