Related papers: Quaternionic toric manifolds

The recent definition of slice regular function of several quaternionic variables suggests a new notion of quaternionic manifold. We give the definition of quaternionic regular manifold, as a space locally modeled on $\mathbb{H}^n$, in a…

This paper introduces a quaternionic analogue of toric geometry by developing the theory of local $Q^n := Sp(1)^n$-actions on 4n-dimensional manifolds, modeled on the regular representation. We identify obstructions that measure the failure…

We initiate the study of the generalized quaternionic manifolds by classifying the generalized quaternionic vector spaces, and by giving two classes of nonclassical examples of such manifolds. Thus, we show that any complex symplectic…

Quaternionic tori are defined as quotients of the skew field $\mathbb{H}$ of quaternions by rank-4 lattices. Using slice regular functions, these tori are endowed with natural structures of quaternionic manifolds (in fact quaternionic…

Delzant's theorem for symplectic toric manifolds says that there is a one-to-one correspondence between certain convex polytopes in $\mathbb{R}^n$ and symplectic toric $2n$-manifolds, realized by the image of the moment map. I review proofs…

This paper introduces the notion of twisted toric manifolds which is a generalization of one of symplectic toric manifolds, and proves the weak Delzant type classification theorem for them. The computation methods for their fundamental…

A theorem of Delzant states that any symplectic manifold $(M,\om)$ of dimension $2n$, equipped with an effective Hamiltonian action of the standard $n$-torus $\T^n = \R^{n}/2\pi\Z^n$, is a smooth projective toric variety completely…

This paper introduces two-dimensional diagrams that are slight generalizations of moment map images for toric four-manifolds and catalogs techniques for reading topological and symplectic properties of a symplectic four-manifold from these…

For the quaternionic unit ball $\mathbb{B}$, let us denote by $\mathcal{M}(\mathbb{B})$ the set of slice regular M\"obius transformations mapping $\mathbb{B}$ onto itself. We introduce a smooth manifold structure on…

The satisfactory development of Quaternionic Analysis has indicated new solutions for physical and mathematical problems. It is worth mentioning the fact that quaternions possess four dimensions, and in this way they may be considered as…

Motivated by the quaternionic geometry corresponding to the homogeneous complex manifolds endowed with (holomorphically) embedded spheres, we introduce and initiate the study of the `quaternionic-like manifolds'. These contain, as…

We introduce the notion of CR quaternionic map and we prove that any such real-analytic map, between CR quaternionic manifolds, is the restriction of a quaternionic map between quaternionic manifolds. As an application, we prove, for…

We define toric contact manifolds in arbitrary codimension and give a description of such manifolds in terms of a kind of labelled polytope embedded into a grassmannian, analogous to the Delzant polytope of a toric symplectic manifold.

In a general and non metrical framework, we introduce the class of CR quaternionic manifolds containing the class of quaternionic manifolds, whilst in dimension three it particularizes to, essentially, give the conformal manifolds. We show…

We construct toric manifolds of complex dimension $\geq 4$, whose orbit spaces by the action of the compact torus are not homeomorphic to simple polytopes (as manifolds with corners). These provide the first known examples of toric…

We investigate slice-quaternionic Hopf surfaces. In particular, we construct new structures of slice-quaternionic manifold on $\mathbb{S}^1\times\mathbb{S}^7$, we study their group of automorphisms and their deformations.

We introduce a natural notion of quaternionic map between almost quaternionic manifolds and we prove the following, for maps of rank at least one: 1) A map between quaternionic manifolds endowed with the integrable almost twistorial…

This paper establishes the basis of the quaternionic differential geometry ($\mathbbm H$DG) initiated in a previous article. The usual concepts of curves and surfaces are generalized to quaternionic constraints, as well as the curvature and…

We study the moment maps of a smooth projective toric variety. In particular, we characterize when the moment map coming from the quotient construction is equal to a weighted Fubini-Study moment map. This leads to an investigation into…

We study $\mathrm{Spin}(7)$-manifolds with an effective multi-Hamiltonian action of a four-torus. On an open dense set, we provide a Gibbons-Hawking type ansatz that describes such geometries in terms of a symmetric $4\times4$-matrix of…