arXiv research

The paper studies a new structure on contact manifolds and its foliation properties.

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 generally richer compared to the 3-Sasakian subclass. In fact, it turns out that t…

The paper solves a 5-manifold foliation problem using a Sasaki-Ricci flow.

Study classifies quasi-Sasakian 3-manifolds, linking them to Sasakian and co-Kähler structures.

Hodge numbers of Sasakian manifolds remain unchanged under deformations.

Study develops geodesic theory for foliations, proving Laplacian comparison theorems.

Study of 3D trans-Sasakian manifolds using Newman--Penrose formalism.

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. Sasakian manifolds are odd dimensional counterparts of Kählerian manifolds to w…

We obtain geometric characterizations of isospectral minimal Riemannian Legendre foliations on compact Sasakian manifolds of constant $φ$-sectional curvature.

The paper defines and studies a new type of submersion from Sasakian manifolds.

In the present paper we carry on a systematic study of 3-quasi-Sasakian manifolds. In particular we prove that the three Reeb vector fields generate an involutive distribution determining a canonical totally geodesic and Riemannian foliation. Locally, the leaves of this foliation turn out to be Lie groups: either the o…

Bi-slant submersion generalizes slant and semi-slant submersion.

Deformations of the Reeb flow of a Sasakian manifold as transversely Kähler 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 of compatible Sasakian metrics for given small deformations of the Reeb flow as tra…

The Hitchin-Kobayashi correspondence is extended to foliated Riemannian manifolds.

Paper confirms Hamilton-Tian conjecture for specific Sasakian manifolds.

We prove that any non-Sasakian contact metric (κ,μ)-space admits a canonical η-Einstein Sasakian or η-Einstein paraSasakian metric. An explicit expression for the curvature tensor fields of those metrics is given and we find the values of κand μfor which such metrics are Sasaki-Einstein and paraSasaki-Einstein. Convers…

We study Riemannian foliations whose transverse Levi-Civita connection $\nabla$ has special holonomy. In particular, we focus on the case where $Hol(\nabla)$ is contained either in SU(n) or in Sp(n). We prove a Weitzenbock formula involving complex basic forms on Kähler foliations and we apply this formula for pointing…

We prove an Atiyah-Bott-Berline-Vergne type localization formula for Killing foliations in the context of equivariant basic cohomology. As an application, we localize some Chern-Simons type invariants, for example the volume of Sasakian manifolds and secondary characteristic classes of Riemannian foliations, to the uni…

The study proves estimates for transverse nonlinear equations on Sasakian manifolds with applications in geometry.

We develop some pluripotential theoretic techniques for the transversally holomorphic foliation of a Sasakian manifold. We prove the convexity of the K-energy along weak geodesics for Sasakian manifolds. This implies that the K-energy is bounded below if a constant scalar curvature structure exists with those metrics m…

Study Higgs bundles and flat connections on quasi-regular Sasakian manifolds.

Study geometric properties of SGL submanifolds in a specific manifold.

The paper introduces new metric structures on $\mathfrak{g}$-foliations and uses a flow to deform them.

In this paper we study the foliated structure of a contact metric $(κ,μ)$-space. In particular, using the theory of Legendre foliations, we give a geometric interpretation to the Boeckx's classification of contact metric $(κ,μ)$-spaces and we find necessary conditions for a contact manifold to admit a compatible contac…

The paper shows convergence of Sasaki-Ricci flow on Sasakian 5-manifolds.

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

The basic Dolbeault cohomology groups of a Sasakian manifold M are invariants of its characteristic foliation F (the orbit foliation of the Reeb flow). We show some fundamental properties of this cohomology, which are useful for its computation. In the first part of the article, we show that the basic Hodge numbers, th…

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

The paper studies critical maps of a specific energy functional on pseudo-Hermitian manifolds.

Study on stability of Sasaki structures under deformations.

The study constructs associative 3-folds in squashed 3-Sasakian manifolds.

The paper studies maps from pseudo-Hermitian to Kähler manifolds, proving harmonic map properties.

We characterize biharmonic anti-invariant surfaces in $3$-dimensional generalized $(κ, μ)$-manifolds with non-zero constant mean curvature by means of the scalar curvature of the ambient space and the mean curvature. In addition, we give a method for constructing infinity many examples of biharmonic submanifolds in a c…

Study radial processes in sub-Riemannian Brownian motions, proving stochastic completeness and eigenvalue estimates.

Study immersions of Sasakian manifolds into Sasakian space forms.

In this paper, we give a new lower bound for the eigenvalues of the Dirac operator on a compact spin manifold. This estimate is motivated by the fact that in its limiting case a skew-symmetric tensor (see Equation \eqref{eq:16}) appears that can be identified geometrically with the O'Neill tensor of a Riemannian flow, …

Paper studies invariant submanifolds in Sasakian spaces, finding conditions for total geodesy.

Spinorially constructs Sasakian and 3-Sasakian structures in arbitrary dimensions.

Study of Sasakian immersions in Heisenberg group and $\mathbb{B}^N imes \mathbb{R}$, focusing on $η$-Einstein case.

We show that the contact reduction can be specialized to Sasakian manifolds. We link this Sasakian reduction to Kähler reduction by considering the Kähler cone over a Sasakian manifold. We present examples of Sasakian manifolds obtained by $S^1$ reduction of standard Sasakian spheres.

Study of CR-submanifolds in various Lorentzian manifolds.

The paper examines *-Ricci tensor properties on Sasakian manifolds.

Defines generalized Sasakian structures in contact geometry.

Study on lightlike geometry in indefinite Sasakian statistical manifolds.

New proof confirms nearly Sasakian condition for high-dimensional manifolds.

Study para-Sasakian φ-symmetric spaces using Boothby-Wang fibration.

We construct the moduli space of contact instantons, an analogue of Yang-Mills instantons defined for contact metric $5$-manifolds and initiate the study of their structure. In the $K$-contact case we give sufficient conditions for smoothness of the moduli space away from reducible connections and show the dimension is…

The study examines properties of quasi-Para-Sasakian manifolds and their curvature.