Related papers: Complexification and hypercomplexification of mani…

The notions of the interior and truncated connections of a nonholonomic manifold are introduced. A class of extended truncated connections is distinguished. For the case of a contact space with a Finsler metric, it is shown that there…

A contact hypersurface in a Kaehler manifold is a real hypersurface for which the induced almost contact metric structure determines a contact structure. We carry out a systematic study of contact hypersurfaces in Kaehler manifolds. We then…

We study complexities of 3-manifolds defined from triangulations, Heegaard splittings, and surgery presentations. We show that these complexities are related by linear inequalities, by presenting explicit geometric constructions. We also…

The solutions to the Euler-Poisson equations are geodesic lines of $SO(3)$ manifold with the metric determined by the inertia tensor. However, the Poisson structure on the corresponding symplectic leaf does not depend on the inertia tensor.…

This paper begins the study of relations between Riemannian geometry and global properties of contact structures on 3-manifolds. In particular we prove an analog of the sphere theorem from Riemannian geometry in the setting of contact…

We describe a supersymmetric generalization of the construction of Kontsevich and Arbarello, De Concini, Kac, and Procesi, which utilizes a relation between the moduli space of curves with the infinite-dimensional Sato Grassmannian. Our…

Let (M,g) be an oriented Lorentzian 4-manifold, and consider the space S of oriented, unparameterized time-like 2-surfaces in M (string world-sheets) with fixed boundary conditions. Then the infinite-dimensional manifold S carries a natural…

We introduce a natural-valued complexity c(X) for pairs X=(M,L), where M is a closed orientable 3-manifold and L is a link contained in M. The definition employs simple spines, but for well-behaved X's we show that c(X) equals the minimal…

We apply the technique of twisted extensions of infinite-dimensional Lie algebras to find new 3D integrable {\sc pde}s related to the deformations of Lie algebra $\mathbb{R}_N[s]\otimes \mathfrak{w}$ with $N=1, 2$ as well as to the Lie…

We give a method to lift $(2,0)$-tensors fields on a manifold $M$ to build symplectic forms on $TM$. Conversely, we show that any symplectic form $\Om$ on $TM$ is symplectomorphic, in a neighborhood of the zero section, to a symplectic form…

In this paper, we study the complex structures of complete hyperk\"ahler four-manifolds of infinite topological type arising from the Gibbons-Hawking ansatz. We show that for almost all complex structures in the hyperk\"ahler family, the…

A C-symplectic structure is a complex-valued 2-form which is holomorphically symplectic for an appropriate complex structure. We prove an analogue of Moser's isotopy theorem for families of C-symplectic structures and list several…

The twistor space \Z of an oriented Riemannian 4-manifold M admits a natural 1-parameter family of Riemannian metrics h_t compatible with the almost complex structures J_1 and J_2 introduced, respectively, by Atiyah, Hitchin and Singer, and…

Let $\bar{L}_i\lr X_i$ be a holomorphic line bundle over a compact complex manifold for $i=1,2$. Let $S_i$ denote the associated principal circle-bundle with respect to some hermitian inner product on $\bar{L}_i$. We construct complex…

We introduce the notion of a rank-3 generalized Clifford manifold, defined by a triple of generalized complex structures satisfying Clifford-type relations. We show that every such structure canonically induces a generalized hypercomplex…

This is the first of two companion papers in which a thorough study of the normal form and the first integrability conditions arising from {\em bi-conformal vector fields} is presented. These new symmetry transformations were introduced in…

We perform the maximal twist of eleven-dimensional supergravity. This twist is partially topological and exists on manifolds of $G_2 \times SU(2)$ holonomy. Our derivation starts with an explicit description of the Batalin-Vilkovisky…

Let X be a complex Fano-manifolds with second Betti-number 1 which carries a contact structure. It follows from previous work that such a manifold can always be covered by lines. Thus, it seems natural to consider the geometry of lines in…

We study almost K\"ahler manifolds whose curvature tensor satisfies the second curvature condition of Gray (shortly ${\cal{AK}}_2$). This condition is interpreted in terms of the first canonical Hermitian connection. It turns out that this…

The space of the associative commutative hyper complex numbers, H_4, is a 4-dimensional metric Finsler space with the Berwald-Moor metric. It provides the possibility to construct the tensor fields on the base of the analytical functions of…