Related papers: On the integrability of the co-CR quaternionic str…

Over the complex numbers, the complement of a collection of hyperplanes is a widely-studied object; the cohomology ring, in particular, is known to have a structure depending only on the combinatorial properties of the intersection of…

We obtain a locally symmetric Kaehler Einstein structure on a tube in the nonzero cotangent bundle of a Riemannian manifold of positive constant sectional curvature. The obtained Kaehler Einstein structure cannot have constant holomorphic…

This survey presents some recent results by the authors and Polterovich on the topological properties of ruled symplectic manifolds. The bundle M \to P \to B that is associated with a ruled manifold has the group of Hamiltonian…

New heterotic torsional geometries are constructed as orbifolds of T^2 bundles over K3. The discrete symmetries considered can be freely-acting or have fixed points and/or fixed curves. We give explicit constructions when the base K3 is…

A cone structure on a complex manifold $M$ is a closed submanifold $\mathcal C \subset \mathbb P TM$ of the projectivized tangent bundle which is submersive over $M$. A conic connection on $\mathcal C$ specifies a distinguished family of…

A contact manifold $M$ can be defined as a quotient of a symplectic manifold $X$ by a proper, free action of $\R^{>0}$, with the symplectic form homogeneous of degree 2. If $X$ is, in addition, Kaehler, and its metric is also homogeneous of…

We study smooth bundles over surfaces with highly connected almost parallelizable fiber $M$ of even dimension, providing necessary conditions for a manifold to be bordant to the total space of such a bundle and showing that, in most cases,…

We consider perturbations of CR structures which preserve the complex tangent bundle. For a compact generic CR manifold its concavity properties and hence the finiteness of some $\overline\partial_b$-cohomology groups are also preserved by…

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…

Given a vector bundle $A\to M$ we study the geometry of the graded manifolds $T^*[k]A[1]$, including their canonical symplectic structures, compatible Q-structures and Lagrangian Q-submanifolds. We relate these graded objects to classical…

The paper develops the fundamentals of quaternionic holomorphic curve theory. The holomorphic functions in this theory are conformal maps from a Riemann surface into the 4-sphere, i.e., the quaternionic projective line. Basic results such…

Let $X$ be a CR manifold with transversal, proper CR $G$-action. We show that $X/G$ is a complex space such that the quotient map is a CR map. Moreover the quotient is universal, i.e. every invariant CR map into a complex manifold…

Let V be the pseudo-Euclidean vector space of signature (p,q), p>2 and W a module over the even Clifford algebra Cl^0 (V). A homogeneous quaternionic manifold (M,Q) is constructed for any spin(V)-equivariant linear map \Pi : \wedge^2 W \to…

In this paper we introduce the twistor space of a Riemannian manifold with an even Clifford structure. This notion generalizes the twistor space of quaternion-Hermitian manifolds and weak-Spin(9) structures. We also construct almost complex…

The base space of a semi-universal unfolding of a hypersurface singularity carries a rich geometric structure, which was axiomatized as a CDV-structure by C. Hertling. For any CDV-structure on a Frobenius manifold M, the pull-back of the…

We study positive definite quaternionic contact $(4n+3)$-manifolds ($qc$-manifold for short). Just like the $CR$-structure contains the class of Sasaki manifolds, the $qc$-structure admits a class of $3$-Sasaki manifolds with integrable…

In this paper we study cobordism categories consisting of manifolds which are endowed with geometric structure. Examples of such geometric structures include symplectic structures, flat connections on principal bundles, and complex…

The purpose of this paper is two-fold: On the one side we would like to close a gap on the classification of vector bundles over $5$-manifolds. Therefore it will be necessary to study quaternionic line bundles over $5$-manifolds which are…

Let $E$ be a vector bundle over a smooth curve $C$, and $V$ a generating space of sections of $E$. We characterise Mumford linear stability of the associated projective model of $\mathbb{P} E^\vee$ in $\mathbb{P} V^\vee$ in terms of…

We analyze quantum correlations and quantum coherence in neutrino oscillations. To this end, we exploit complete complementarity relations (CCR) that fully characterize the interplay between different correlations encoded in a quantum…