Related papers: Universal unfoldings of Laurent polynomials and tt…

In this work, the warped product of Hamilton spaces is introduced and it is shown that these spaces obtain Hamiltonian structure as well. Then, the geometric properties of warped product Hamilton spaces such as their nonlinear connections…

Given a hypercomplex manifold with a rotating vector field (and additional data), we construct a conical hypercomplex manifold. As a consequence, we associate a quaternionic manifold to a hypercomplex manifold of the same dimension with a…

We formalize the ``metric bundle'' viewpoint by defining, for any smooth $n$--manifold $M$, the open fiberwise cones $\mathcal{G}^{p,q}\subset S^2\Tstar M$ of nondegenerate symmetric bilinear forms with fixed signature $(p,q)$, and we…

We investigate the universal cover of projective threefolds whose tangent bundle is a direct sum of subbundles in case the Kodaira dimension is not 1 and 2. We also prove results on Fano manifolds with splitting tangent bundles in any…

The Frobenius manifold structure on the space of rational functions with multiple simple poles is constructed. In particular, the dependence of the Saito-flat coordinates on the flat coordinates of the intersection form is studied. While…

For any compact Lie group $G$ and any $n$ we construct a smooth $G$-manifold $U_n(G)$ such that any smooth $n$-dimensional $G$-manifold can be embedded in $U_n(G)$ with a trivial normal bundle. Furthermore, we show that such embeddings are…

We present a survey on the moduli spaces of rank 2 quadric bundles over a compact Riemann surface X. These are objects which generalise orthogonal bundles and which naturally occur through the study of the connected components of the moduli…

Motivated by generalized geometry, we discuss differential geometric structures on the total space $\mathfrak{T}M$ of the bundle $TM\oplus T^*M$, where $M$ is a differentiable manifold; $\mathfrak{T}M$ is called a big-tangent manifold. The…

Fix a simple complex Lie group G and a principal sl(2,C) subalgebra of Lie(G). Then the moduli space of semi-stable, topologically trivial G-Higgs bundles on a hyperbolic, spin Riemann surface acquires a marked point. This is the unique…

The Tango bundle T over P^5 is proved to be the pull-back of the twisted Cayley bundle C(1) via a map f : P^5 --> Q_5 existing only in characteristic 2. The Frobenius morphism F factorizes via such f. Using f the cohomology of T is computed…

Let (M,I,J,K) be a compact hypercomplex manifold admitting an HKT-metric. Assume that the canonical bundle of (M,I) is trivial as a holomorphic line bundle. We show that the holonomy of Obata connection on M is contained in SL(n,H). In…

There are theories of coverings of $C^*$-algebras which can be included into a following list: coverings of commutative $C^*$-algebras, coverings of $C^*$-algebras of groupoids and foliations, coverings of noncommutative tori, the double…

We show that the moduli space of simple flat bundles over a compact Sasakian manifold is a finite disjoint union of moduli spaces of simple flat bundles with fixed basic structures. This gives a detailed description of the non-abelian Hodge…

On a complex manifold, a co-Higgs bundle is a holomorphic vector bundle with an endomorphism twisted by the tangent bundle. The notion of generalized holomorphic bundle in Hitchin's generalized geometry coincides with that of co-Higgs…

We put into light some generalized almost quaternionic and almost para-quaternionic structures and characterize their integrability with respect to a $\nabla$-bracket on the generalized tangent bundle $TM\oplus T^*M$ of a smooth manifold…

F-theory admits 7-branes with exceptional gauge symmetries, which can be compactified to give phenomenological four-dimensional GUT models. Here we study general supersymmetric compactifications of eight-dimensional Yang-Mills theory. They…

We review the origin of the physical consistency of the Lorentz- Poincar\'e symmetry. We outline seemingly catastrophic physical inconsistencies recently identified for noncanonical-nonunitary generalized theories defined on conventional…

This review paper is concerned with the generalizations to field theory of the tangent and cotangent structures and bundles that play fundamental roles in the Lagrangian and Hamiltonian formulations of classical mechanics. The paper…

A generalization of the Hartogs theorem is proved for a class of Tubes structures. We assume that the intervening commutative Lie algebra admits at least a number of globally solvable generators greater or equal to the structure…

We study the relations between the triviality of the tangent bundle $TM$ and the generalized tangent bundle $\mathbb{T}M = TM\oplus T^*M$ of a manifold. We show that the generalized tangent bundle of a paralellizable manifold is trivial. We…