Related papers: Remark on quasi Sasakian structures
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.…
This paper is devoted to the study of curvature and torsion of almost contact curves in trans-Sasakian 3-Manifolds. The conditions for the frenet curves to be almost contact curves in trans-Sasakian 3-manifolds have been obtained.
Deformations of the Reeb flow of a Sasakian manifold as transversely K\"ahler flows may not admit compatible Sasakian metrics anymore. We show that the triviality of the (0,2)-component of the basic Euler class characterizes the existence…
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…
A Sasakian manifold is a Riemannian manifold whose metric cone admits a certain K\"ahler structure which behaves well under homotheties. We show that the product of two compact Sasakian manifolds admits a family of complex structures…
We show that $3$-Sasaki structures admit a natural description in terms of projective differential geometry. This description provides a concrete link between $3$-Sasaki structures and several other geometries and constructions via a single…
Weak contact metric manifolds, i.e., the linear complex structure on the contact distribution is replaced by a nonsingular skew-symmetric tensor, defined by the author and R. Wolak, allowed us to take a new look at the theory of contact…
We define a contact metric structure on the manifold corresponding to a second order ordinary differential equation $d^2y/dx^2=f(x,y,y')$ and show that the contact metric structure is Sasakian if and only if the 1-form $\frac{1}{2}(dp-fdx)$…
We study the Sasaki cone of a CR structure of Sasaki type on a given closed manifold. We introduce an energy functional over the cone, and use its critical points to single out the strongly extremal Reeb vectors fields. Should one such…
We classify simply connected compact Sasaki manifolds of dimension $2n+1$ with positive transverse bisectional curvature. In particular, the K\"ahler cone corresponding to such manifolds must be bi-holomorphic to $\C^{n+1}\backslash \{0\}$.…
Almost contact complex Riemannian manifolds, known also as almost contact B-metric manifolds, are in principle equipped with a pair of mutually associated pseudo-Riemannian metrics. Each of these metrics is specialized here as a Yamabe…
Mixed 3-structures are odd-dimensional analogues of paraquaternionic structures. They appear naturally on lightlike hypersurfaces of almost paraquaternionic hermitian manifolds. We study invariant and anti-invariant submanifolds in a…
Every compact 3-Sasakian 7-manifold $M$ admits a canonical 2-parameter family of co-closed $\text{G}_2$-structures $\varphi_{a,b}$ for $a,b > 0$, as well as a foliation by $\varphi_{a,b}$-associative 3-folds whose leaf space $X$ is a…
A contact manifold $M$ can be defined as a quotient of a symplectic manifold $X$ by a proper, free action of $\R^{>0}$, with the symplectic form homogeneous of degree 2. If $X$ is, in addition, Kaehler, and its metric is also homogeneous of…
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,…
For an almost contact metric manifold $N$, we find conditions for which either the total space of an $S^1$-bundle over $N$ or the Riemannian cone over $N$ admits a strong K\"ahler with torsion (SKT) structure. In this way we construct new…
We classify locally homogeneous quasi-Sasakian manifolds in dimension five that admit a parallel spinor $\psi$ of algebraic type $F \cdot \psi = 0$ with respect to the unique connection $\nabla$ preserving the quasi-Sasakian structure and…
We continue the program of Chinea, De Leon and Marrero who studied the topology of cosymplectic manifolds. We study 3-cosymplectic manifolds which are the closest odd-dimensional analogue of hyper-Kaehler structures. We show that there is…
We describe various constructions in Sasakian geometry. First we generalize the join construction of the first two authors to arbitrary Sasakian manifolds. We then give several examples, including ones which prove the existence of…
We collect our recent results ([5] and [8]) and we get the equivalence of the three notions of the title under some conditions. We then use this equivalence in order to prove some consequences about Sasakian manifolds, complex almost…