arXiv research

Study finds submaximal symmetries in almost quaternionic structures.

Resolves gap problem for quaternion-Hermitian structures.

The conformal infinity of a quaternionic-Kahler metric on a 4n-manifold with boundary is a codimension 3-distribution on the boundary called quaternionic contact. In dimensions 4n-1 greater than 7, a quaternionic contact structure is always the conformal infinity of a quaternionic-Kahler metric. On the contrary, in dim…

New spaces identified with specific properties.

Positive Quaternion Kaehler Manifolds are Riemannian manifolds with holonomy contained in Sp(n)Sp(1) and with positive scalar curvature. Conjecturally, they are symmetric spaces. We prove this conjecture in dimension 20 under additional assumptions and we provide recognition theorems for quaternionic projective spaces …

Study local control in a 7D quaternionic Heisenberg group.

Study quaternionic Bott-Chern cohomology and HKT metrics existence.

The study finds conditions for quaternionic structures on symmetric spaces.

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 example, that for any submanifold $M$, of dimension $4k-1$, of a quaternionic manifold…

Defines quaternionic k-vector fields on quaternionic Kähler manifolds.

We prove that a compact quaternionic-Kähler manifold of dimension $4n\geq 8$ admitting a conformal-Killing 2-form which is not Killing, is isomorphic to the quaternionic projective space, with its standard quaternionic-Kähler structure.

Finite volume ends found in quaternionic Kähler manifolds.

New growth rate identified for quaternionic Heisenberg group filling functions.

We investigate the integrability of almost complex structures on the twistor space of an almost quaternionic manifold constructed with the help of a quaternionic connection. We show that if there is an integrable structure it is independent on the quaternionic connection. In dimension four, we express the anti-self-dua…

Study eigenvalue estimates on Kähler and quaternion Kähler manifolds.

Local classification of quaternion-Kähler metrics with rotating $S^1$-symmetry.

New construction generalizes quaternionic Kähler/hyper-Kähler correspondence.

We prove that if the fundamental 4-form of an almost-quaternionic Hermitian manifold (M, Q, g) of dimension at least eight satisfies the conformal-Killing equation, then (M, Q, g) is quaternionic-Kahler.

Study counts and equidistributes rational points in quaternionic Heisenberg groups.

Symplectic 4-manifolds with Kodaira dimension zero can be viewed as symplectic Calabi-Yau surfaces. We are able to completely determine their Betti numbers by proving two general results on quaternionic vector bundles.

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 that these manifolds have a rich natural Twistor Theory and, along the way, we o…

We classify, up to orbit equivalence, all cohomogeneity one actions on the hyperbolic planes over the complex, quaternionic and Cayley numbers, and on the complex hyperbolic spaces of dimension greater than two. For the quaternionic hyperbolic spaces of dimension greater than two we reduce the classification problem to…

We investigate the integrability of natural almost complex structures on the twistor space of an almost para-quaternionic manifold as well as the integrability of natural almost paracomplex structures on the reflector space of an almost para-quaternionic manifold constructed with the help of a para-quaternionic connect…

The paper classifies compact affine quaternionic curves and surfaces.

In a general and non metrical framework, we introduce the class of co-CR quaternionic manifolds, which contains the class of quaternionic manifolds, whilst in dimension three it particularizes to give the Einstein-Weyl spaces. We show that these manifolds have a rich natural Twistor Theory and, along the way, we obtain…

In this paper we show that the Ray-Singer complex analytic torsion is trivial for even dimensional Calabi-Yau manifolds. Then we define the quaternionic analytic torsion for quaternionic manifolds and prove that they are metric independent. In dimension four, the quaternionic analytic torsion equals to the self-dual an…

New quaternionic toric manifolds introduced, studied with properties.

We study the moduli space of quaternionic Kaehler structures on a compact manifold of dimension 4n (n>2) from a point of view of Riemannian geometry, not twistor theory. Then we obtain a rigidity theorem for quaternionic Kaehler structures of nonzero scalar curvature by observing the moduli space.

We show that the fundamental 4-form on a quaternionic contact manifold of dimension at least eleven is closed if and only if the torsion endomorphism of the Biquard connection vanishes. This condition characterizes quaternionic contact structures which are locally qc homothetic to 3-Sasakian structures.

Lower bounds for quaternionic hyperbolic orbifold volumes found.

Paper constructs an example of a non-compact submanifold in a quaternionic Kähler symmetric space.

The paper establishes correspondences between quaternionic spinors, Minkowski flags, and hyperbolic horospheres.

Almost hypercomplex manifolds with Hermitian and Norden metrics and more specially the corresponding quaternionic Kaehler manifolds are considered. Some necessary and sufficient conditions the investigated manifolds be isotropic hyper-Kaehlerian and flat are found. It is proved that the quaternionic Kaehler manifolds w…

The paper studies smooth structures on quaternionic projective spaces using inertia groups.

A complete solution to the quaternionic contact Yamabe equation on the qc sphere of dimension $4n+3$ as well as on the quaternionic Heisenberg group is given. A uniqueness theorem for the qc Yamabe problem in a compact locally 3-Sasakian manifold is shown.

Abstract: Generalizes supergravity c-map to quaternionic manifolds.

Proves local existence of quaternionic contact structures using Cartan-Kähler theory.

We classify the holomorphic structures of the tangent vertical bundle T of the twistor fibration of a quaternionic manifold (M,Q) of dimension bigger than four. In particular, we show that any self-dual quaternionic connection on (M, Q) induces an holomorphic structure on T. We prove that the positive tensor powers of …

Almost para-quaternionic structures on smooth manifolds of dimension $2n$ are equivalent to almost Grassmannian structures of type $(2,n)$. We remind the equivalence and exhibit some interrelations between subjects that were previously studied independently from the para-quaternionic and the Grassmannian point of view.…

We review the general properties of target spaces of hypermultiplets, which are quaternionic-like manifolds, and discuss the relations between these manifolds and their symmetry generators. We explicitly construct a one-to-one map between conformal hypercomplex manifolds (i.e. those that have a closed homothetic Killin…

We show that a 1-parameter family Ricci flow ancient solutions arises from the natural collapsings of the twistor space of positive quaternion Kähler manifolds. We use these ancient solutions to show that a positive quaternion Kähler manifold is isometric to one of the Wolf spaces.

The study classifies homogeneous Sasaki manifolds over quaternionic Kähler spaces.

The paper examines the topology of quaternionic toric actions on manifolds.

The spaces of Sp(n)-, Sp(n)U(1)- and Sp(n)Sp(1)- invariant, translation invariant, continuous convex valuations on the quaternionic vector space H^n are studied. Combinatorial dimension formulas involving Young diagrams and Schur polynomials are proved.

The paper establishes sub-gradient estimates and entropy formulas for quaternionic contact geometry heat equations.

Study on quaternionic Kähler manifolds and their integrable Hermitian structures.

On 7D quaternionic contact manifolds, eigenvalue bounds imply special structure.

Study eigenvalues on quaternion-Kähler manifolds with geometric bounds.