Related papers: Some examples of toric Sasaki-Einstein manifolds
The question of whether a Sasakian metric can admit an additional compatible (K-)contact structure is addressed. In the complete case if the second structure is also assumed Sasakian, works of Tachibana-Yu and Tanno show that the manifold…
The orthogonal decomposition of the Webster curvature provides us a way to characterize some canonical metrics on a pseudo-Hermitian manifold. We derive some subelliptic differential inequalities from the Weitzenb\"ock formulas for the…
We review our study of Sasakian geometry as an agent for proving the existence of Einstein metrics on odd dimensional manifolds. Particular emphasis is given to the Sasakian structures occuring on links of isolated hypersurface…
We produce infinite families of SKT manifolds by using methods of toric geometry like the $J$-construction. These SKT manifolds are total spaces of certain principal $G$-bundles over smooth projective toric varieties, where $G$ is an even…
We construct new examples of non-formal simply connected compact Sasaki-Einstein 7-manifolds. We determine the minimal model of the total space of any fibre bundle over $CP^2$ with fibre $S^1\times S^2$ or $S^3/Z_p$ ($p>0$), and we apply…
We provide a general method to construct examples of quasi-Sasakian 3-structures on a (4n+3)-dimensional manifold. Moreover, among this class, we give the first explicit example of a compact 3-quasi-Sasakian manifold which is not the global…
We prove that closed simply connected $5$-manifolds $2(S^2\times S^3)\# nM_2$ allow Sasaki-Einstein structures, where $M_2$ is the closed simply connected $5$-manifold with $\mathrm{H}_2(M_2,\mathbb{Z})=\mathbb{Z}/2\mathbb{Z}\oplus…
Let $L_f$ be a link of an isolated hypersurface singularity defined by a weighted homogenous polynomial $f.$ In this article, we give ten examples of $2$-connected seven dimensional Sasaki-Einstein manifolds $L_f$ for which $H_{3}(L_f,…
In this paper we show that any good toric contact manifold has well defined cylindrical contact homology and describe how it can be combinatorially computed from the associated moment cone. As an application we compute the cylindrical…
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…
We show that toric geometry can be used rather effectively to translate a brane configuration to geometry. Roughly speaking the skeletons of toric space are identified with the brane configurations. The cases where the local geometry…
We prove that every nearly Sasakian manifold of dimension greater than five is Sasakian. This provides a new criterion for an almost contact metric manifold to be Sasakian. Moreover, we classify nearly cosymplectic manifolds of dimension…
We give criterions for the existence of toric conical Kahler-Einstein and Kahler-Ricci soliton metrics on any toric manifold in relation to the greatest Ricci and Bakry-Emery-Ricci lower bound. We also show that any two toric manifolds with…
We study complete, simply-connected manifolds with special holonomy that are toric with respect to their multi-moment maps. We consider the cases where there is a connected non-Abelian symmetry group containing the torus. For…
The Hessian geometry is the real analogue of the K\"ahler one. Sasakian geometry is an odd-dimensional counterpart of the K\"ahler geometry. In the paper, we study the connection between projective Hessian and Sasakian manifolds analogous…
Recent renewed interest in Sasakian manifolds is due mainly to the fact that they can provide examples of generalized Einstein manifolds, manifolds which are of great interest in mathematical models of various aspects of physical phenomena.…
In the same way that a contact manifold determines and is determined by a symplectic cone, a Sasaki manifold determines and is determined by a suitable Kahler cone. Kahler-Sasaki geometry is the geometry of these cones. This paper presents…
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…
In this paper, we show that the uniform L^{4}-bound of the transverse Ricci curvature along the Sasaki-Ricci flow on a compact quasi-regular Sasakian (2n+1)-manifold M of general type. As an application, any solution of the normalized…
We show that every toric Sasaki-Einstein manifold $S$ admits a special Legendrian submanifold $L$ which arises as the link ${\rm fix}(\tau)\cap S$ of the fixed point set ${\rm fix}(\tau)$ of an anti-holomorphic involution $\tau$ on the cone…