The study lifts certain Sasakian manifolds to quasi-Einstein spacetimes.
problem Understanding lifts of Sasakian manifolds to quasi-Einstein spacetimes.
method Analyzing smooth Sasakian manifolds and their lifts to 4D quasi-Einstein spacetimes.
result Smooth Sasakian manifolds can be lifted to quasi-Einstein shearfree spacetimes of Petrov type II or D.
The paper finds exact solutions to a complex Einstein-Dirac-Maxwell system on 4D Sasakian spacetimes.
problem Finding exact solutions to an Einstein-Dirac-Maxwell system with Sasakian quasi-Killing spinors.
method Constructing a family of exact solutions on four-dimensional static Sasakian spacetimes using the Sasakian frame.
result Closed and open universe models are found with specific energy conditions.
Study immersions of Sasakian manifolds into Sasakian space forms.
problem Characterize Sasakian manifolds that can be immersed into Sasakian space forms.
method Proved Calabi's rigidity results, characterised homogeneous Sasakian manifolds.
result Characterized homogeneous Sasakian manifolds that can be embedded into the standard sphere.
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 of Sasakian immersions in Heisenberg group and BNimesR, focusing on η-Einstein case.
problem Classification of Sasakian immersions in specific spaces.
method Analysis of complete regular Sasakian manifolds in Heisenberg group and BNimesR with standard Sasakian structures. result Complete classification of η-Einstein Sasakian immersions. The object of this paper is to study the invariant submanifolds of Sasakian generalized-Sasakian-space-form. Here, we obtain some equivalent conditions for an invariant submanifold of a Sasakian generalized-Sasakian-space-forms to be totally geodesic.
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 S1 reduction of standard Sasakian spheres.
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 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.
Study on lightlike geometry in indefinite Sasakian statistical manifolds.
problem Exploring lightlike hypersurfaces and their properties in indefinite Sasakian statistical manifolds.
method Introducing indefinite Sasakian statistical manifolds and analyzing lightlike hypersurfaces with respect to dual connections.
result An invariant lightlike submanifold of an indefinite Sasakian statistical manifold is itself an indefinite Sasakian statistical manifold.
Study para-Sasakian φ-symmetric spaces using Boothby-Wang fibration.
problem Characterize para-Sasakian φ-symmetric spaces.
method Use Boothby-Wang fibration to construct and provide examples.
result Explicit construction and example of para-Sasakian φ-symmetric spaces.
Sasakian immersions prove Sasaki-Ricci solitons are η-Einstein with rational constants.
problem Understanding local immersions of Sasaki-Ricci solitons into Sasakian space forms.
method Analyzing local Sasakian immersions and proving η-Einstein properties.
result Sasaki-Ricci solitons are η-Einstein with rational constants under certain conditions.
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.
The purpose of this paper is to study *-Ricci tensor on Sasakian manifold. Here, φ-confomally flat and confomally flat *-η-Einstein Sasakian manifold are studied. Next, we consider *-Ricci symmetric conditon on Sasakian manifold. Finally, we study a special type of metric called *-Ricci soliton on Sasakian manifold.
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.
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 curvature is necessarily either 3-α-Sasakian or 3-cosymplectic.
The aim of this paper is to study Sasakian immersions of compact Sasakian manifolds into the odd-dimensional sphere equipped with the standard Sasakian structure. We obtain a complete classification of such manifolds in the Einstein and η-Einstein cases when the codimension of the immersion is 4. Moreover, we exhib…
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.
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 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.
We show certain symmetry of the dimensions of cohomologies of the funda- mental groups of compact Sasakian manifolds by using the Hodge theory of twisted basic cohomology. As applications, we show that the polycyclic fundamental groups of compact Sasakian manifolds are virtually nilpotent and Sasakian solvmanifolds are…
Simplified proofs and new distributions on anti-quasi-Sasakian manifolds.
problem Properties of anti-quasi-Sasakian manifolds.
method Simplified proofs and discussion of new invariant distributions.
result New invariant distributions exist on every anti-quasi-Sasakian manifold.
Nilpotent Sasakian manifolds are Heisenberg nilmanifolds.
problem Characterizing Sasakian manifolds with nilpotent fundamental groups.
method Proved diffeomorphism to Heisenberg nilmanifolds.
result Compact aspherical Sasakian manifolds with nilpotent fundamental groups are Heisenberg nilmanifolds.
Paper confirms Hamilton-Tian conjecture for specific Sasakian manifolds.
problem Hamilton-Tian conjecture for specific Sasakian manifolds.
method Sasaki-Ricci flow, compact transverse Fano Sasakian 5-manifolds, klt foliation singularities.
result Confirmed Hamilton-Tian conjecture for compact transverse Fano Sasakian 5-manifolds.
The orthogonal decomposition of the Webster curvature provides us a way to characterize some canonical metrics on a pseudo-Hermitian manifold. We derive some subelliptic differential inequalities from the Weitzenböck formulas for the traceless pseudo-Hermitian Ricci tensor and the Chern-Moser tensor of Sasakian manifol…
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…
Study properties of 3D trans-Sasakian manifolds with η-Yamabe solitons.
problem Properties of 3D trans-Sasakian manifolds with η-Yamabe solitons.
method Investigated curvature conditions and constructed a manifold.
result Construct a 3D trans-Sasakian manifold satisfying η-Yamabe soliton.
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.
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.
In this paper we study the 3-dimensional (ε)-para Sasakian manifolds. We obtain an necessary and sufficient condition for an (ε)-para Sasakian 3 -manifold to be an indefinite space form. We show that a Ricci-semi-symmetric (ε)-para Sasakian 3 -manifold is an indefinite space form…
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.
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…
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.
Study on 3D trans-Sasakian manifolds with η-Einstein solitons.
problem Characterizing 3D trans-Sasakian manifolds with η-Einstein solitons.
method Analyzing properties of Codazzi type and cyclic parallel Ricci tensors on 3D trans-Sasakian manifolds.
result Examples and properties of 3D trans-Sasakian manifolds with η-Einstein solitons.
We prove that every nearly Sasakian manifold of dimension greater than five is Sasakian. This provides a new criterion for an almost contact metric manifold to be Sasakian. Moreover, we classify nearly cosymplectic manifolds of dimension greater than five.
Study Higgs bundles and flat connections on quasi-regular Sasakian manifolds.
problem Investigate Higgs bundles and flat connections on compact Sasakian manifolds.
method Introduce quasi-regularity and regularity of vector bundles, relate to orbibundles, extend non-abelian Hodge correspondence.
result Extend non-abelian Hodge correspondence to quasi-regular Sasakian manifolds.
We consider some natural infinitesimal Einstein deformations on Sasakian and 3-Sasakian manifolds. Some of these are infinitesimal deformations of Killing spinors and further some integrate to actual Killing spinor deformations. In particular, on 3-Sasakian 7 manifolds these yield infinitesimal Einstein deformations pr…
Study on LP-Sasakian manifolds with generalized η-Ricci solitons.
problem Properties of LP-Sasakian manifolds with generalized η-Ricci solitons.
method Investigation of LP-Sasakian manifolds with generalized η-Ricci solitons associated to the general connection.
result Existence of generalized η-Ricci solitons on a 4-dimensional LP-Sasakian manifold.
Local Sasaki-Ricci solitons are η-Einstein in certain fiber products of homogeneous Sasakian manifolds.
problem Characterizing local immersions of Sasaki-Ricci solitons into homogeneous Sasakian manifolds.
method Analyzing local Sasakian immersions of Sasaki-Ricci solitons into fiber products of homogeneous Sasakian manifolds.
result Sasaki-Ricci solitons are η-Einstein in certain fiber products of homogeneous Sasakian manifolds. We investigate some topological properties, in particular formality, of compact Sasakian manifolds. Answering some questions raised by Boyer and Galicki, we prove that all higher (than three) Massey products on any compact Sasakian manifold vanish. Hence, higher Massey products do obstruct Sasakian structures. Using th…
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. We complete the reduction of Sasakian manifolds with the non-zero case by showing that Willett's contact reduced space is compatible with the Sasakian structure. We then prove the compatibility of the non-zero Sasakian (in particular, contact) reduction with the reduction of the Kähler (in particular, symplectic) cone.…
Study Hodge theory and supersymmetry on Sasakian and Vaisman manifolds.
problem Decomposing harmonic forms and cohomology on Sasakian and Vaisman manifolds.
method Construct Lie superalgebra, use Hodge decomposition, compute supersymmetry algebra.
result Explicit computation of the supersymmetry algebra of Sasakian manifolds.
Approximates compact and non-compact Sasakian manifolds in spheres.
problem Approximating Sasakian structures in spheres.
method CR immersions in standard spheres.
result Compact and non-compact Sasakian manifolds can be approximated.
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.
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…
Study biharmonic hypersurfaces in Sasakian space form using Tanaka-Webster connection.
problem Exploring biharmonic hypersurfaces in Sasakian space form.
method Using Tanaka-Webster connection to study biharmonic hypersurfaces.
result Developed new insights into biharmonic hypersurfaces in Sasakian space form.
We show that on a Sasakian 3-sphere the Sasaki-Ricci flow initiating from a Sasakian metric of positive transverse scalar curvature converges to a gradient Sasaki- Ricci soliton. We also show the existence and uniqueness of gradient Sasaki-Ricci soliton on each Sasakian 3-sphere.