Related papers: Mixed 3-Sasakian structures and curvature

3-quasi-Sasakian manifolds were recently studied by the authors as a suitable setting unifying 3-Sasakian and 3-cosymplectic geometries. In this paper some geometric properties of this class of almost 3-contact metric manifolds are briefly…

A 3-dimensional Riemannian manifold equipped with a tensor structure of type $(1,1)$, whose third power is the identity, is considered. This structure and the metric have circulant matrices with respect to some basis, i.e., these structures…

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 find some curvature properties of 3-quasi-Sasakian manifolds which are similar to some well-known identities holding in the Sasakian case. As an application, we prove that any 3-quasi-Sasakian manifold of constant horizontal sectional…

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…

We describe a method to obtain $\mathrm{SU}(3)$-structures and $\mathrm{G}_2$-structures on 6 and 7-dimensional manifolds respectively, such that its associated metric is Einstein. More concretely, we have that different classes of…

In this paper, we introduce the trans-para-Sasakian manifolds and we study their geometry. These manifolds are an analogue of the trans-Sasakian manifolds in the Riemannian geometry. We shall investigate many curvature properties of these…

We consider a 3-dimensional Riemannian manifold M with two circulant structures -- a metric g and an endomorphism q whose third power is identity. The structure q is compatible with g such that an isometry is induced in any tangent space of…

Many authors have studied Ricci solitons and their analogs within the framework of (almost) contact geometry. In this article, we thoroughly study the $(m,\rho)$-quasi-Einstein structure on a contact metric manifold. First, we prove that if…

We study the sectional curvature of plane distributions on 3-manifolds. We show that if the distribution is a contact structure it is easy to manipulate this curvature. As a corollary we obtain that for every transversally oriented contact…

In this paper the notion of quasi-isometry between two Riemannian manifolds has been introduced. This idea is also imposed to study quasi-isometry between two almost contact metric manifolds. Moving further, some curvature properties of two…

We study manifolds endowed with mixed metric 3--contact structures, proving that the distribution spanned by the Reeb vector fields is integrable, with totally geodesic integral manifolds, of constant sectional curvature $k=\pm1$. We also…

This paper begins the study of relations between Riemannian geometry and global properties of contact structures on 3-manifolds. In particular we prove an analog of the sphere theorem from Riemannian geometry in the setting of contact…

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…

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…

3-quasi-Sasakian manifolds were studied systematically by the authors in a recent paper as a suitable setting unifying 3-Sasakian and 3-cosymplectic geometries. This paper throws new light on their geometric structure which reveals to be…

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…

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.

The Newman-Penrose-Perjes formalism is applied to smooth contact structures on riemannian 3-manifolds. In particular it is shown that a contact 3-manifold admits an adapted riemannian metric if and only if it admits a metric with a…

We study eta-Einstein geometry as a class of distinguished Riemannian metrics on contact metric manifolds. In particular, we use a previous solution of the Calabi problem for Sasakian geometry to prove the existence of eta-Einstein…