Defines generalized Sasakian structures in contact geometry.
problem Understanding k-contact manifolds and CR manifolds.
method Introduced generalized Sasakian structures and proved their equivalence to Sasakian structures.
result k-contact manifolds are generalized Sasakian if and only if they are classically Sasakian.
Spinorially constructs Sasakian and 3-Sasakian structures in arbitrary dimensions.
problem Constructing Sasakian and 3-Sasakian structures in arbitrary dimensions.
method Spinorial construction and analysis of invariant spinors.
result Complete description of invariant spinors on homogeneous 3-Sasakian spaces.
Study classifies quasi-Sasakian 3-manifolds, linking them to Sasakian and co-Kähler structures.
problem Classifying quasi-Sasakian structures in 3-manifolds.
method Deformation-based approach examining foliation and basic cohomology.
result Every quasi-Sasakian structure in this setting can be deformed into a Sasakian or co-Kähler one.
Defines a new Poisson structure for generalized Sasakian spaces.
problem No specific problem stated; focuses on new structure definition.
method Defines a canonical Poisson structure on generalized contact metric spaces.
result Shows distinction between generalized Sasakian and coKähler structures.
Researchers found all invariant contact structures on tangent sphere bundles of compact symmetric spaces.
problem Identifying all invariant contact metric structures on tangent sphere bundles of compact rank-one symmetric spaces.
method Explicitly obtained all structures, distinguishing K-contact, Sasakian, and 3-Sasakian structures.
result There is a unique Sasakian-Einstein metric on tangent sphere bundles of spheres and real projective spaces.
The paper characterizes Sasakian manifolds using weak nearly Sasakian structures.
problem Characterizing Sasakian manifolds using a new structure.
method Study of weak nearly Sasakian structures and proving theorems.
result Provides a new criterion for a weak almost contact metric manifold to be Sasakian.
Researchers provide explicit parametrizations for Sasakian space forms.
problem Understanding homogeneous contact Riemannian structures on Sasakian space forms.
method Explicit parametrizations of all homogeneous structures.
result Detailed descriptions of all homogeneous structures in 3D Sasakian space forms.
New metric structures generalize Sasakian and cosymplectic structures, proving rigidity and finding conditions.
problem Generalizing Sasakian and cosymplectic structures to new metric structures.
method Introducing weak structures and proving rigidity of Sasakian structures.
result Any weak Sasakian structure is homothetically equivalent to a Sasakian structure.
Complex structures found on product of Sasakian manifolds.
problem Exploring complex structures on the product of two Sasakian manifolds.
method Examined a family of complex structures on the product of two compact Sasakian manifolds, computed Dolbeault cohomology groups.
result None of the complex structures in the family admit compatible locally conformally Kähler metrics if both Sasakian manifolds are of dimension greater than 1.
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 structures. We obtain a generalized Sasakian structure on a non-compact manifold which…
The study examines extensions of Lie algebras with specific geometric structures.
problem Conditions for preserving geometric structures in Lie algebra extensions.
method Analyzes extensions of Sasakian and Frobenius-Kähler Lie algebras.
result Conditions for maintaining Sasakian or Frobenius-Kähler structures after extensions.
Study on negative Sasakian structures on specific 5-manifolds.
problem Existence of negative Sasakian structures on simply-connected 5-manifolds.
method Analysis of rational homology spheres and Smale-Barden manifolds.
result Proves existence of negative Sasakian structures on specific 5-manifolds.
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 Sasakian manifolds. As a consequence, any nearly Sasakian manifold is a contact ma…
In this paper we deal with two classes of mixed metric 3-structures, namely the mixed 3-Sasakian structures and the mixed metric 3-contact structures. Firstly we study some properties of the curvature of mixed 3-Sasakian structures, proving that any manifold endowed with such a structure is Einstein. Then we prove the …
Geometric flows study nearly parallel G2-structures on 3-Sasakian 7-manifolds.
problem Analyzing geometric flows of G2-structures on 3-Sasakian manifolds.
method Study of Laplacian flow and Laplacian coflow of G2-structures on 3-Sasakian manifolds.
result Distinct behavior of flows, notably regarding stability of nearly parallel G2-structures.
Study η-Einstein Sasakian structures on Lie algebras, dividing cases based on center dimension.
problem Investigate η-Einstein Sasakian structures on Lie algebras. method Divide cases based on center dimension, use theory of normal j-algebras and modifications of Hermitian Lie algebras to construct examples. result Construct new examples of η-Einstein Sasakian Lie algebras and solvmanifolds. Study shows compact Sasakian manifolds are locally Heisenberg up to deformation.
problem Characterizing compact Sasakian manifolds.
method Analyzing basic Chern classes and using left invariant Sasakian structures.
result Compact Sasakian manifolds are locally isomorphic to the real Heisenberg group.
First example of a 5D manifold with K-contact but no Sasakian structure.
problem Long-standing question of Boyer and Galicki about existence of Sasakian structures.
method Construction of a specific 5-manifold.
result First example of a simply connected compact 5-manifold with K-contact but no Sasakian structure.
Any Sasakian structure can be closely mimicked by embeddings into weighted spheres.
problem Approximating Sasakian structures on closed manifolds.
method Using CR embeddings into weighted Sasakian spheres and strengthening previous approximation results.
result Sasakian structures can be approximated in the Cq-norm by embeddings into weighted Sasakian spheres. The paper studies a new structure on contact manifolds and its foliation properties.
problem Investigating a new structure on contact manifolds.
method Examining weak nearly Sasakian structures and their foliations.
result The weak nearly Sasakian structure foliates into two types of totally geodesic foliations.
The Hessian geometry is the real analogue of the Kähler one. Sasakian geometry is an odd-dimensional counterpart of the Kähler geometry. In the paper, we study the connection between projective Hessian and Sasakian manifolds analogous to the one between Hessian and Kähler manifolds. In particular, we construct a Sasaki…
Study on harmonicity of complex structure on product of trans-Sasakian manifolds.
problem Investigating harmonicity of complex structure on product of trans-Sasakian manifolds.
method Analysis of Levi-Civita connection and conditions for harmonicity on product manifold.
result Conditions for harmonicity of complex structure on product manifold of trans-Sasakian manifolds.
Study on a specific type of Lie algebras with Kähler and contact properties.
problem Characterizing and classifying transversely Kähler almost contact metric Lie algebras.
method Analyzing properties of Lie algebras with contact forms and Kähler structures, considering center dimensions and quotient properties.
result Classification of 5-dimensional η-Einstein transversely Kähler almost contact metric Lie algebras.
The paper defines a new connection on sub-Riemannian manifolds and explores conditions for almost quasi-Sasakian manifolds to be Einstein.
problem Exploring new connections and conditions for specific types of manifolds.
method Defining a skew-symmetric connection and studying its properties on sub-Riemannian manifolds, and examining conditions for almost quasi-Sasakian manifolds to be Einstein.
result Sufficient conditions are found for an almost quasi-Sasakian manifold to be an Einstein manifold.
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 Sasakian-Einstein metrics on manifolds homeomorphic to S2×S5. Then we use a gen…
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 must be 3-Sasakian or an odd dimensional sphere with constant curvature. Some ext…
New constructions of Sasakian and K-contact structures on Smale-Barden manifolds.
problem Deciding when a Smale-Barden manifold admits a Sasakian or K-contact structure.
method Developing quasi-regular Seifert fibrations and applying them to constructions.
result Determined all Smale-Barden manifolds admitting null Sasakian structures and provided counterexamples to conjectures.
The paper constructs Sasakian lifts from Kähler manifolds and studies their properties.
problem Constructing Sasakian structures from Kähler manifolds and analyzing their geometric properties.
method Local construction of Sasakian manifolds from Kähler base using vector field operations.
result Existence and properties of α-Sasakian Ricci solitons in Sasakian lifts. The present paper is devoted to quasi-Para-Sasakian manifolds. Basic properties of such manifolds are obtained and general curvature identities are investigated. Next it is proved that if M is quasi-Para-Sasakian manifold of constant curvature K. Then K ≤0 and (i) if K=0, the manifold is paracosymplecti…
Kollár has found subtle obstructions to the existence of Sasakian structures on 5-dimensional manifolds. In the present article we develop methods of using these obstructions to distinguish K-contact manifolds from Sasakian ones. In particular, we find the first example of a closed 5-manifold M with H1(M,Z)=0 which …
We obtain some general results on Sasakian Lie algebras and prove as a consequence that a (2n + 1)-dimensional nilpotent Lie group admitting left-invariant Sasakian structures is isomorphic to the real Heisenberg group H2n+1. Furthermore, we classify Sasakian Lie algebras of dimension 5 and determine which of th…
Study shows lightlike hypersurfaces in indefinite Sasakian manifolds are not symmetric.
problem Characterizing curvature symmetries in lightlike hypersurfaces of indefinite Sasakian manifolds.
method Analyzing properties of lightlike hypersurfaces in indefinite Sasakian manifolds.
result Lightlike hypersurfaces are not locally symmetric, semi-symmetric, or semi-parallel.
Study of instantons on Stiefel manifold with G2 and Sasakian structures.
problem Characterizing and classifying instantons on Stiefel manifold.
method Reductive decomposition, spinorial approach, Weitzenböck-type formula with torsion.
result Classification of invariant connections and rigidity results for G2-instantons. In this article, we introduce some metallic structures on the tangent bundle of a P-Sasakian manifold by complete lift, horizontal lift and vertical lift of a P-Sasakian structure (φ,η,ξ) on tangent bundle. Then we investigate the integrability and parallelity of these metallic structures.
Study 3-Sasakian and G2 structures on manifolds.
problem Investigate algebra of forms on 3-Sasakian manifolds.
method Examine cohomogeneity-one actions on spheres and Berger's space.
result Identify nearly-parallel G2 forms.
Sasakian structures found on tangent sphere bundles of certain symmetric spaces.
problem Existence of Sasakian structures on tangent sphere bundles of compact rank-one symmetric spaces.
method Proof of existence using K-contact structures and induced structures from almost Hermitian structures.
result Tangent sphere bundles of compact rank-one symmetric spaces admit unique K-contact structures that are Sasakian.
Survey of recent progress in Sasakian geometry.
problem Topological properties and existence of Sasakian structures.
method Review of recent research findings.
result Recent progress in Sasakian geometry.
The aim of this paper is to study Sasakian immersions of (non-compact) complete regular Sasakian manifolds into the Heisenberg group and into BN×R equipped with their standard Sasakian structures. We obtain a complete classification of such manifolds in the η-Einstein case.
Extending the work of G. Székelyhidi and T. Brönnle to Sasakian manifolds we prove that a small deformation of the complex structure of the cone of a constant scalar curvature Sasakian manifold admits a constant scalar curvature structure if it is K-polystable. This also implies that a small deformation of the complex …
Uniformizes compact Sasakian manifolds into circle bundles.
problem Deforming compact Sasakian manifolds to locally isomorphic forms.
method Criterion based on circle bundles of anti-canonical bundles over Hermitian symmetric spaces.
result Sasakian manifolds can be deformed to locally isomorphic forms.
Study of 3D trans-Sasakian manifolds using Newman--Penrose formalism.
problem Characterizing and understanding the geometry of 3D trans-Sasakian manifolds.
method Using Newman--Penrose formalism to encode the geometry of the structure vector field.
result Derivation of curvature and Laplacian identities for trans-Sasakian manifolds and their subclasses, including rigidity results.
The aim of this paper is to study compact 5--manifolds which carry a positive Sasakian structure. Strong restrictions are derived for the integral homology groups. In some cases, all positive Sasakian structures are classified. A key step is to study log Del Pezzo surfaces whose boundary divisor contains positive genus…
Study proves no lightlike hypersurfaces exist in certain indefinite Sasakian manifolds.
problem Existence of lightlike hypersurfaces in indefinite Sasakian manifolds.
method Proved non-existence through properties of second fundamental forms and induced structural tensors.
result No lightlike hypersurfaces can have parallel or recurrent second fundamental forms or induced structural tensors.
In this note I study the Sasakian geometry associated to the standard CR structure on the Heisenberg group, and prove that the Sasaki cone coincides with the set of extremal Sasakian structures. Moreover, the scalar curvature of these extremal metrics is constant if and only if the metric has Φ-sectional curvature $-…
We study the Lie algebra of infinitesimal isometries on compact Sasakian and K--contact manifolds. On a Sasakian manifold which is not a space form or 3--Sasakian, every Killing vector field is an infinitesimal automorphism of the Sasakian structure. For a manifold with K--contact structure, we prove that there exists …
In this paper we provide a second variation formula for L-minimal Lagrangian submanifolds in a pseudo-Sasakian manifold. We apply it to the case of Lorentzian-Sasakian manifolds and relate the L-stability of L-minimal Legendrians in a Sasakian M to their L-stability in an associated Lorentzian-Sasakian structure on M.
Introduces pqc structures, generalizing para 3-Sasakian geometry.
problem Generalizing and studying para 3-Sasakian geometry.
method Defines pqc structures, derives a distinguished linear connection, and presents structure equations.
result Para 3-Sasakian spaces are pqc manifolds and pqc-Einstein.
The Newman-Penrose-Perjes formalism is applied to Sasakian 3-manifolds and the local form of the metric and contact structure is presented. The local moduli space can be parameterised by a single function of two variables and it is shown that, given any smooth function of two variables, there exists locally a Sasakian …