arXiv research

Paper confirms Hamilton-Tian conjecture for specific Sasakian manifolds.

New 5-manifolds allow Sasaki-Einstein structures.

New connections on 5-manifolds linked to Sasaki-Einstein structures.

A series of examples of toric Sasaki-Einstein 5-manifolds is constructed. These are submanifolds of toric 3-Sasaki 7-manifolds and such a Sasaki-Einstein 5-manifold corresponds uniquely to a toric 3-Sasaki 7-manifold. This produces examples of quasi-regular Sasaki-Einstein structures on every #k(S^2 xS^3), for k odd. T…

We consider hypersurfaces in Einstein-Sasaki 5-manifolds which are tangent to the characteristic vector field. We introduce evolution equations that can be used to reconstruct the 5-dimensional metric from such a hypersurface, analogous to the (nearly) hypo and half-flat evolution equations in higher dimensions. We use…

The paper solves a 5-manifold foliation problem using a Sasaki-Ricci flow.

We give a correspondence between toric 3-Sasaki 7-manifolds S and certain toric Sasaki-Einstein 5-manifolds M. These 5-manifolds are all diffeomorphic to k#(S^2\times S^3), where k=2b_2(S)+1, and are given by a pencil of Sasaki embeddings of M in S and are given concretely by the zero set of a component of the 3-Sasaki…

The paper shows convergence of Sasaki-Ricci flow on Sasakian 5-manifolds.

We prove the existence of Sasaki-Einstein metrics on certain simply connected 5-manifolds where until now existence was unknown. All of these manifolds have non-trivial torsion classes. On several of these we show that there are a countable infinity of deformation classes of Sasaki-Einstein structures.

We present a general procedure to construct 6-dimensional manifolds with SU(3)-structure from SU(2)-structure 5-manifolds. We thereby obtain half-flat cylinders and sine-cones over 5-manifolds with Sasaki-Einstein SU(2)-structure. They are nearly Kahler in the special case of sine-cones over Sasaki-Einstein 5-manifolds…

The Seiberg-Witten equations are lifted to Kaluza-Klein 5-manifolds.

We study compatible toric Sasaki metrics with constant scalar curvature on co-oriented compact toric contact manifolds of Reeb type of dimension at least 5. These metrics come in rays of transversal homothety due to the possible rescaling of the Reeb vector fields. We prove that there exist Reeb vector fields for which…

We construct the moduli space of contact instantons, an analogue of Yang-Mills instantons defined for contact metric $5$-manifolds and initiate the study of their structure. In the $K$-contact case we give sufficient conditions for smoothness of the moduli space away from reducible connections and show the dimension is…

We carry on a systematic study of nearly Sasakian manifolds. We prove that any nearly Sasakian manifold admits two types of integrable distributions with totally geodesic leaves which are, respectively, Sasakian or $5$-dimensional nearly Sasakian manifolds. As a consequence, any nearly Sasakian manifold is a contact ma…

We prove that any totally geodesic hypersurface $N^5$ of a 6-dimensional nearly Kähler manifold $M^6$ is a Sasaki-Einstein manifold, and so it has a hypo structure in the sense of \cite{ConS}. We show that any Sasaki-Einstein 5-manifold defines a nearly Kähler structure on the sin-cone $N^5\times\mathbb R$, and a compa…

Explicitly constructed 5-manifolds tessellated by prisms.

Heegaard diagrams for 5-manifolds help in understanding their structure.

Smoothly embed 3-manifolds in 5-manifolds, simplifying topological to smooth.

New 5D hyperbolic shapes that wrap around a circle found.

A 5-manifold fibers over a circle with nonpositive curvature.

Complete obstruction found for 2-spheres in 5-manifolds to be isotopic.

The aim of this paper is to study compact 5--manifolds which admit fixed point free circle actions. The first result implies that the torsion in the second homology and the second Stiefel--Whitney class have to satisfy strong restrictions. We then show that for simply connected 5--manifolds these restrictions are neces…

New 5-manifold without 'spine' challenges deformation conjecture.

Smooth 5-manifolds can be decomposed into three pieces.

Exploring Sasaki metrics in joined manifolds.

New 5-manifold found with zero Ricci curvature.

The paper examines Sasaki-Ricci solitons and their transverse rigidity properties.

Resolves singular fibers of a 5-manifold with $S^1$ action.

Using recent work on high dimensional Lutz twists and families of Weinstein structures we show that any almost contact structure on a 5-manifold is homotopic to a contact structure.

Negative curvature proven in Sasaki manifold space completion.

According to Giroux, contact manifolds can be described as open books whose pages are Stein manifolds. For 5-dimensional contact manifolds the pages are Stein surfaces, which permit a description via Kirby diagrams. We introduce handle moves on such diagrams that do not change the corresponding contact manifold. As an …

We consider a fixed contact 3-manifold that admits infinitely many compact Stein fillings which are all homeomorphic but pairwise non-diffeomorphic. Each of these fillings gives rise to a closed contact 5-manifold described as a contact open book whose page is the filling at hand and whose monodromy is the identity sym…

In this paper, an explicit classification result for certain 5-manifolds with fundamental group Z/2 is obtained. These manifolds include total spaces of circle bundles over simply-connected 4-manifolds.

We consider the stability of Sasaki-extremal metrics under deformations of the complex structure on the Reeb foliation. Given such a deformation preserving the action of a compact subgroup of the automorphism group of a Sasaki-extremal structure, a sufficient condition is given involving the nondegeneracy of the relati…

We classify $5$-manifolds with fundamental group $\mathbb Z$ and $π_{2}$ a finitely generated abelian group in terms of the cup product on the second cohomology of the universal covering. The classification result is applied to study simple knots $k \colon S^{3} \subset S^{5}$ and the question, which compact topologica…

Locally homogeneous aspherical Sasaki manifolds are quasi-regular S1-Seifert bundles.

The paper characterizes Pfaffian embeddings from 2,3,5-manifolds to 7-dimensional isotropic spaces.

New curvature for weighted Sasaki sphere found.

The abstract discusses metrics with positive biorthogonal curvature on 5-manifolds.

We make some elementary observations concerning subcritically Stein fillable contact structures on 5-manifolds. Specifically, we determine the diffeomorphism type of such contact manifolds in the case the fundamental group is finite cyclic, and we show that on the 5-sphere the standard contact structure is the unique s…

New approach linking CR Yamabe invariant to Sasaki structures.

The paper explores existence and non-existence of constant scalar curvature and extremal Sasaki metrics.

Study of Sasaki groups vs Kähler groups, showing distinct behaviors.

In this paper we give a diameter bound for Sasaki manifolds with positive transverse Ricci curvature. As an application, we obtain the uniqueness of Sasaki-Einstein metrics on compact Sasaki manifolds modulo the action of the identity component of the automorphism group for the transverse holomorphic structure.

The paper introduces twins in Kähler and Sasaki geometry, generalizing known concepts.

We introduce a holomorphic sheaf E on a Sasaki manifold and study two new notions of stability for E along the Sasaki-Ricci flow related to the `jumping up' of the number of global holomorphic sections of E at infinity. First, we show that if the Mabuchi K-energy is bounded below, the transverse Riemann tensor is bound…

In this paper, we introduce a class of Sasaki manifolds with a reductive $G$-group action, called $G$-Sasaki manifolds. By reducing K-energy to a functional defined on a class of convex functions on a moment polytope, we give a criterion for the properness of K-energy. In particular, we deduce a sufficient and necessar…

We prove some structure results for \emph{transverse reducible} Sasaki manifolds. In particular, we show Sasaki manifolds with positive Ricci curvature is transversely irreducible, and so there is no join (product) construction for irregular Sasaki-Einstein manifolds, as opposed to the quasi-regular case done by Wang-Z…