Related papers: A new construction of homogeneous quaternionic man…

A homogeneous Riemannian space $(M= G/H,g)$ is called a geodesic orbit space (shortly, GO-space) if any geodesic is an orbit of one-parameter subgroup of the isometry group $G$. We study the structure of compact GO-spaces and give some…

We find a principle of harmonic analyticity underlying the quaternionic (quaternion-K\"ahler) geometry and solve the differential constraints which define this geometry. To this end the original $4n$-dimensional quaternionic manifold is…

We study the behavior of connections and curvature under the HK/QK correspondence, proving simple formulae expressing the Levi-Civita connection and Riemann curvature tensor on the quaternionic K\"ahler side in terms of the initial…

These notes record three lectures given at the workshop "Higher symmetries in Physics", held at the Universidad Complutense de Madrid in November 2008. In them we explain how to construct a Lie (super)algebra associated to a spin manifold,…

Given a K\"ahler manifold $M$ endowed with a Hamiltonian Killing vector field $Z$, we construct a conical K\"ahler manifold $\hat{M}$ such that $M$ is recovered as a K\"ahler quotient of $\hat{M}$. Similarly, given a hyper-K\"ahler manifold…

Any pseudo-Hermitian or para-Hermitian manifold of dimension 4 admits a unique Kaehler-Weyl structure; this structure is locally conformally Kaehler if and only if the alternating Ricci tensor vanishes. The alternating Ricci tensor takes…

We show that a compact quaternionic-K\"ahler manifold with positive scalar curvature and nonnegative sectional curvature is isometric to a symmetric space. This extends a classical theorem of Berger.

We find a necessary condition for the existence of an action of a Lie group $G$ by quaternionic automorphisms on an integrable quaternionic manifold in terms of representations of $\mathfrak{g}$. We check this condition and prove that a…

We introduce the class of almost symmetric submanifolds of Euclidean space, a close relative of symmetric submanifolds and (contact) sub-Riemannian symmetric spaces. More specifically, we prove that every full irreducible almost symmetric…

It can be shown that it is possible to find a representation of Hecke algebras within Clifford algebras of multivectors. These Clifford algebras possess a unique gradation and a possibly non-symmetric bilinear form. Hecke algebra…

We study relations between quaternionic Riemannian manifolds admitting different types of symmetries. We show that any hyperKahler manifold admitting hyperKahler potential and triholomorphic action of S^1 can be constructed from another…

A hypercomplex manifold is a manifold equipped with a triple of complex structures $I, J, K$ satisfying the quaternionic relations. We define a quaternionic analogue of plurisubharmonic functions on hypercomplex manifolds, and interpret…

A smooth curve on a homogeneous manifold $G/H$ is called a Riemannian equigeo-desic if it is a homogeneous geodesic for any $G$-invariant Riemannian metric. The homogeneous manifold $G/H$ is called Riemannian equigeodesic, if for any $x\in…

We construct examples of complete quaternionic K\"ahler manifolds with an end of finite volume, which are not locally homogeneous. The manifolds are aspherical with fundamental group which is up to an infinite cyclic extension a semi-direct…

We classify indefinite simply connected hyper-Kaehler symmetric spaces. Any such space without flat factor has commutative holonomy group and signature (4m,4m). We establish a natural 1-1 correspondence between simply connected…

We show that for all very special quaternionic manifolds a different N=1 reduction exists, defining a Kaehler Geometry which is ``dual'' to the original very special Kaehler geometry with metric G_{a\bar{b}}= - \partial_a \partial_b \ln V…

This article discusses the existence problem of a compact quotient of a symmetric space by a properly discontinuous group with emphasis on the non-Riemannian case. Discontinuous groups are not always abundant in a homogeneous space $G/H$ if…

On a para-quaternionic K\"ahler manifold $(\widetilde M^{4n},Q,\widetilde g)$, which is first of all a pseudo-Riemannian manifold, a natural definition of (almost) K\"ahler and (almost) para-K\"ahler submanifold $(M^{2m},\mathcal{J},g)$ can…

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…

A quaternionic K\"ahler manifold M is called {\it positive} if it has positive scalar curvature. The main purpose of this paper is to prove several connectedness theorems for quaternionic immersions in a quaternionic K\"ahler manifold, e.g.…