Related papers: Hartogs phenomenon and the problem of complex sphe…
We investigate solutions of type II supergravity which have the product R^4 x M^6 structure with non-compact M^6 factor and which preserve at least four supersymmetries. In particular, we consider various conifolds and the N=1…
We show that there is no complex structure in a neighborhood of the space of orthogonal almost complex structures on the sphere $S^{2n}, \ n>1$. The method is to study the first Chern class of vetcor bundle $T^{(1,0)}S^{2n}$.
The existence of some complex geometrical structures on a compact manifold such as complex structures, Kaehler (pseudo-Kaehler) structures often impose certain restrictions on its underling topological or differentiable manifold. In this…
We show that there is an almost complex structure on a differential calculus on finite points coming from a bidirected finite graph without multiple edges or loops. We concentrate on a polygon as a concrete case. In particular, a…
We show that any almost complex structure, positively tamed with $\omega$ on nearly K\"{a}hler 6-manifold $(M,g,J,\omega)$ is not integrable
In this paper, we study the complexity factor for a charged anisotropic self-gravitating object. We formulate the Einstein-Maxwell field equations, Tolman-Opphenheimer-Volkoff equation, and the mass function. We form the structure scalars…
Let (J,g) be a Hermitian structure on a compact nilmanifold M with invariant complex structure J and compatible metric g, which is not required to be invariant. We give classifications of 6-dimensional nilmanifolds M admitting strong…
Heisenberg-like spins lying on the pseudosphere (a 2-dimensional infinite space with constant negative curvature) cannot give rise to stable soliton solutions. Only fractional solutions can be stabilized on this surface provided that at…
Using elliptic fibrations with specific singular fibers, we find spheres with very negative self-intersections in elliptic surfaces and in their blow-ups.
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…
We explain in some detail the geometric structure of spheres in any dimension. Our approach may be helpful for other homogeneous spaces (with other signatures) such as the de Sitter and anti-de Sitter spaces. We apply the procedure to the…
In this note, we answer in negative a question posed by McGibbon about the generic property of H-space structure. In fact we verify the conjecture of Roitberg. Incidentally, the same example also answers in negative the open problem 10 in…
A completely reducible subcomplex of a spherical building is a spherical building.
Spherical coverings on the S2 sphere and their algebraic numbers are given for the putatively optimal global solutions for some n-congruent spherical caps with minimal radius to completely cover the S2 sphere. A few locally optimal…
We show that near densest-packing the perturbations of the HCP structure yield higher entropy than perturbations of any other densest packing. The difference between the various structures shows up in the correlations between motions of…
We compute the Ozsv\'ath--Szab\'o contact invariants for all tight contact structures on the manifolds -\Sigma(2,3,6n-1).
The hedgehog Skyrme model on three-sphere admits very rich spectrum of solitonic solutions which can be encompassed by a strikingly simple scheme. The main result of this paper is the statement of the tripartite structure of solutions of…
The classification of isoparametric hypersurfaces in spheres with four or six different principal curvatures is still not complete. In this paper we develop a structural approach that may be helpful for a classification. Instead of working…
We compute the cohomology of the unordered configuration spaces of the sphere $S^2$ with integral and with $\mathbb{Z}/p \mathbb{Z}$-coefficients using a cell complex by Fuks, Vainshtein and Napolitano.
The space $\mathcal{Z}$ of leftinvariant orthogonal almost complex structures, keeping the orientation, on 6-dimensional Lie groups is researched. To get explicit view of this space elements the isomorphism of $\mathcal{Z}$ and…