arXiv research

Negative curvature proven in Sasaki manifold space completion.

The study classifies homogeneous Sasaki manifolds over quaternionic Kähler spaces.

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

Study on deforming Sasaki-Einstein metrics on $T^{1,1}$ space.

Sasaki manifolds have isometric spaces of potentials implying similar geometric properties.

Sphere theorems for submanifolds in Kähler and Sasaki spaces.

The paper studies Sasaki-Ricci solitons on Sasakian manifolds up to seven dimensions.

The paper proves the existence of Sasaki-Einstein metrics on specific Sasakian manifolds.

Quantizes geodesics in Kähler and Sasaki geometry.

We show that the standard picture regarding the notion of stability of constant scalar curvature metrics in Kähler geometry described by S.K. Donaldson, which involves the geometry of infinite-dimensional groups and spaces, can be applied to the constant scalar curvature metrics in Sasaki geometry with only few modific…

We show that the Einstein-Hilbert functional, as a functional on the space of Reeb vector fields, detects the vanishing Sasaki-Futaki invariant. In particular, this provides an obstruction to the existence of a constant scalar curvature Sasakian metric. As an application we prove that K-semistable polarized Sasaki mani…

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…

We extend profound results in pluripotential theory on Kahler manifolds to Sasaki setting via its transverse Kahler structure. As in Kahler case, these results form a very important piece to solve the existence of Sasaki metrics with constant scalar curvature (cscs) in terms of properness of K-energy. One main result i…

Study of coupled Sasaki-Einstein and solitons metrics.

We find a Sasaki-Einstein metric from a CFT state in AdS5.

We obtain infinite classes of new Einstein-Sasaki metrics on complete and non-singular manifolds. They arise, after Euclideanisation, from BPS limits of the rotating Kerr-de Sitter black hole metrics. The new Einstein-Sasaki spaces L^{p,q,r} in five dimensions have cohomogeneity 2, and U(1) x U(1) x U(1) isometry group…

Sasakian immersions prove Sasaki-Ricci solitons are η-Einstein with rational constants.

Study local moduli of Sasaki-Einstein metrics on specific polynomial links.

Constructs moduli spaces for Calabi-Yau cones and Sasaki-Einstein manifolds.

We prove a uniform Sobolev inequality along the Sasaki-Ricci flow. In the process, we develop the theory of basic Lebesgue and Sobolev function spaces, and prove some general results about the decomposition of the heat kernel for a class of elliptic operators on a Sasaki manifold.

New spinorial field equation reveals geometric properties of Sasaki manifolds.

In this paper we study the Sasakian geometry on S^3-bundles over a Riemann surface of genus g>0 with emphasis on extremal Sasaki metrics. We prove the existence of a countably infinite number of inequivalent contact structures on the total space of such bundles that admit 2-dimensional Sasaki cones each with a Sasaki m…

New examples of non-formal Sasaki-Einstein 7-manifolds and their submanifolds found.

The paper classifies Sasaki-Einstein orbits in compact Hermitian symmetric spaces.

The study examines the stability of Einstein metrics on Sasaki Einstein and nearly parallel G2 manifolds.

Exploring Sasaki metrics in joined manifolds.

New Einstein metrics found from para-Sasaki-like Riemannian manifolds.

Study on stability of minimal submanifolds in specific Einstein manifolds.

New cohomology $η$ for deformed Sasaki-Einstein manifolds derived from Dolbeault cohomology.

Study curvature properties of a specific type of Sasaki manifolds.

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

Classifies invariant spinors on nine sphere types.

Local Sasaki-Ricci solitons are $η$-Einstein in certain fiber products of homogeneous Sasakian manifolds.

Several Einstein-Sasaki 7-metrics appearing in the physical literature are fibered over four dimensional Kahler-Einstein metrics. Instead we consider here the natural Kahler-Einstein metrics defined over the twistor space Z of any quaternion Kahler 4-space, together with the corresponding Einstein-Sasaki metrics. We wo…

We study null Sasakian structures in dimension five. First, based on a result due to Kollár [Ko], we improve a result by Boyer, Galicki and Matzeu in [BGM] and prove that simply connected manifolds diffeomorphic to $# k(S^2\times S^3)$ admit null Sasaki $η$-Einstein structures if and only if $k\in \{3,..., 21\}$. After…

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…

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…

New curvature for weighted Sasaki sphere found.

New approach linking CR Yamabe invariant to Sasaki structures.

Let $M$ be a closed manifold of Sasaki type. A polarization of $M$ is defined by a Reeb vector field, and for one such, we consider the set of all Sasakian metrics compatible with it. On this space, we study the functional given by the squared $L^2$-norm of the scalar curvature. We prove that its critical points, or ca…

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.

Equivalence found between certain Kahler and Sasaki metrics.

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…