相关论文: Constructions in Sasakian Geometry
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…
The main purpose of this work is to generalize the $S^3_\bfw$ Sasaki join construction $M\star_\bfl S^3_\bfw$ described in \cite{BoTo14a} when the Sasakian structure on $M$ is regular, to the general case where the Sasakian structure is…
By combining the join construction from Sasakian geometry with the Hamiltonian 2-form construction from K\"ahler geometry, we recover Sasaki-Einstein metrics discovered by physicists. Our geometrical approach allows us to give an algorithm…
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…
We study 5-dimensional Riemannian manifolds that admit an almost contact metric structure. In particular, we generalize the class of quasi-Sasaki manifolds and characterize these structures by their intrinsic torsion. Among other things, we…
Using the Sasakian join construction with homology 3-spheres, we give a countably infinite number of examples of Sasakian manifolds with perfect fundamental group in all odd dimensions greater than 1. These have extremal Sasaki metrics with…
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…
We describe a general procedure for constructing new Sasaki metrics of constant scalar curvature from old ones. Explicitly, we begin with a regular Sasaki metric of constant scalar curvature on a 2n+1-dimensional compact manifold M and…
In the seminal book of Boyer and Galicki "Sasakian Geometry" the authors formulated a research program of studying topological properties and answering questions about the existence of Sasakian structures. We survey recent progress in this…
In previous work (arXiv:2205.12067), we defined a notion of a generalized Sasakian structure in the context of generalized contact geometry, the odd dimensional analogue of generalized complex geometry introduced by Hitchin and Gualtieri.…
We introduce generalized almost contact structures which admit the $B$-field transformations on odd dimensional manifolds. We provide definition of generalized Sasakain structures from the view point of the generalized almost contact…
Using $S^1$-equivariant symplectic homology, in particular its mean Euler characteristic, of the natural filling of links of Brieskorn-Pham polynomials, we prove the existence of infinitely many inequivalent contact structures on various…
The join construction produces a third Sasaki manifold from two others, and we investigate the algebraic topology of the joins of circle bundles over surfaces of positive genus with weighted three-spheres. Topologically, such a join has 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…
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.…
We discuss a deformation of Sasakian structure in the presence of totally skew-symmetric torsion by introducing odd dimensional manifolds whose metric cones are K\"ahler with torsion. It is shown that such a geometry inherits similar…
The purpose of this paper is to study reducibility properties in Sasakian geometry. First we give the Sasaki version of the de Rham Decomposition Theorem; however, we need a mild technical assumption on the Sasaki automorphism group which…
This is an expository paper, which provides a first introduction to geometric structures on $TM\oplus T^*M$. The paper contains definitions and characteristic properties of generalized complex, generalized Kaehler, generalized (normal,…
We discuss Sasakian-Einstein geometry under a quasi-regularity assumption. It is shown that the space of all quasi-regular Sasakian-Einstein orbifolds has a natural multiplication on it. Furthermore, necessary and sufficient conditions are…
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…