Related papers: Twistor spaces on foliated manifolds
We study tautness properties of a Riemannian foliation by investigating a symmetric 2-tensor associated with the mean curvature of the foliation. As a consequence, we prove a tautness condition for Riemannian foliations on compact manifolds…
A hyperk\"ahler manifold is defined as a Riemannian manifold endowed with three covariantly constant complex structures that are quaternionically related. A twistor space is characterized as a holomorphic fiber bundle $p: \mathcal{Z}…
A hyperkaehler manifold with a circle action fixing just one complex structure admits a natural a hyperholomorphic line bundle. This forms the basis for the construction of a corresponding quaternionic Kaehler manifold in the work of…
Consider a singular Riemannian foliation (s.r.f for short) on a compact manifold. By successive blow-ups along the strata, we construct a regular Riemannian foliation on another compact Riemannian manifold and a desingularization map that…
Toric orbifolds are a topological generalization of projective toric varieties associated to simplicial fans. We introduce some sufficient conditions on the combinatorial data associated to a toric orbifold to ensure the existence of an…
We prove Wilking's Conjecture about the completeness of dual leaves for the case of Riemannian foliations on nonnegatively curved symmetric spaces. Moreover, we conclude that such foliations split as a product of trivial foliations and a…
We use quilted Floer theory to construct functor-valued invariants of tangles arising from moduli spaces of flat bundles on punctured surfaces. As an application, we show the non-triviality of certain elements in the symplectic mapping…
Given a manifold M with a submanifold N, the deformation space D(M,N) is a manifold with a submersion to R whose zero fiber is the normal bundle, and all other fibers are equal to M. This article uses deformation spaces to study the local…
The twistor method is applied for obtaining examples of generalized Kaehler structures which are not yielded by Kaehler structures.
In this work a proposal for definition of twistors on generic curved spaces is exposed and investigated. We consider superpositions of nearly autoparallel and nearly geodesic maps (nearly conformal maps, nc-maps) of (pseudo-)Riemannian…
We give a short introduction to the theory of twisted Alexander polynomials of a 3--manifold associated to a representation of its fundamental group. We summarize their formal properties and we explain their relationship to twisted…
The space of topological decompositions into triangulations of a surface has a natural graph structure where two triangulations share an edge if they are related by a so-called flip. This space is a sort of combinatorial Teichm\"uller space…
We consider contact foliations: objects which generalise to higher dimensions the flow of the Reeb vector field on contact manifolds. We list a number of properties of such foliations, and propose two conjectures about the topological types…
We describe a class of topological field theories called ``balanced topological field theories.'' These theories are associated to moduli problems with vanishing virtual dimension and calculate the Euler character of various moduli spaces.…
We define a diffeology on the Milnor classifying space of a diffeological group $G$, constructed in a similar fashion to the topological version using an infinite join. Besides obtaining the expected classification theorem for smooth…
Learning in Riemannian orbifolds is motivated by existing machine learning algorithms that directly operate on finite combinatorial structures such as point patterns, trees, and graphs. These methods, however, lack statistical…
The mixed scalar curvature is one of the simplest curvature invariants of a foliated Riemannian manifold. We explore the problem of prescribing the mixed scalar curvature of a foliated Riemann-Cartan manifold by conformal change of the…
We study aspects of 3d $\mathcal{N}=2$ supersymmetric gauge theories on the product of a line and a Riemann surface. Performing a topological twist along the Riemann surface leads to an effective supersymmetric quantum mechanics on the…
Let M be a hyperk\"ahler manifold. The S^2-family of complex structures compatible with the hyperk\"ahler metric can be assembled into a single complex structure on Z=MxS^2; the resulting complex manifold is known as the twistor space of M.…
In this note, we find the conditions on an odd-dimensional Riemannian manifolds under which its twistor space is eta-Einstein.