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.
New 5D manifold found without certain Sasakian structure.
problem Finding a 5D manifold without specific Sasakian structure.
method Constructing symplectic 4-manifold and proving Betti number bound.
result First example of 5D manifold with K-contact but no semi-regular Sasakian structure.
The study finds a continuous map achieving minmax area under Legendrian constraints.
problem Finding minmax areas under Legendrian constraints in 5D Sasakian manifolds.
method Continuous conformal Legendrian map with bounded multiplicity satisfying a weak Hamiltonian Minimal Equation.
result Continuous map achieving minmax area with bounded multiplicity.
Study invariant CKY 2-forms on 5D Lie groups, classifying and determining their properties.
problem Classifying and understanding CKY 2-forms on 5D Lie groups.
method Classification and analysis of 5D metric Lie algebras with CKY tensors.
result First examples of CKY 2-forms on metric Lie algebras without Sasakian structures.
New G2-holonomy manifolds from 5d N=1 theories domain walls.
problem Geometrizing domain walls in 5d N=1 theories.
method Constructing 7-manifolds by fibering a Calabi-Yau over a real line.
result 7-manifolds with G2-holonomy from domain walls in 5d theories. Novel gauge-theoretic Floer homologies defined from 5d N=2 theory, linking 4, 3, and 2-manifolds.
problem Defining and linking novel Floer homologies for different manifold dimensions.
method Physics of a topologically-twisted 5d N=2 gauge theory, Vafa-Witten, Hitchin, and BF configurations.
result Derived novel gauge-theoretic and symplectic Floer homologies, and Atiyah-Floer correspondences.
Inequality found for a specific equation on 5D manifolds.
problem Finding an inequality for a Yamabe type equation on 5D manifolds.
method Analyzing a Yamabe type equation in 5D manifolds.
result An inequality of type sup x inf found for the Yamabe type equation in 5D.
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.
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.
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.
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.
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.
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.
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.
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 explore 4d Yang-Mills gauge theories (YM) living as boundary conditions of 5d gapped short/long-range entangled (SRE/LRE) topological states. Specifically, we explore 4d time-reversal symmetric pure YM of an SU(2) gauge group with a second-Chern-class topological term at θ=π (SU(2)θ=π YM), by turning on backg…
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.
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.
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.
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…
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.
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…
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 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.
Paper classifies structures on 5D manifolds with specific rank and conditions.
problem Classifying tangent distributions on 5D manifolds.
method Established necessary and sufficient topological condition for existence.
result Classification of structures up to homotopy as formal Cartan distributions.
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.
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.
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.
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. 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.
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…
No complete Einstein hypersurfaces found in a specific type of Sasakian manifold.
problem Existence of Einstein hypersurfaces in Sasakian manifolds.
method Non-existence proof for complete, Einstein hypersurfaces tangent to the Reeb vector field.
result No complete Einstein hypersurfaces found in the specified Sasakian manifold.
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…
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…
We provide a general method to construct examples of quasi-Sasakian 3-structures on a (4n+3)-dimensional manifold. Moreover, among this class, we give the first explicit example of a compact 3-quasi-Sasakian manifold which is not the global product of a 3-Sasakian manifold and a hyper-Kähler manifold.
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.
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…
In this paper we study *-Conformal η-Ricci soliton on Sasakian manifolds. Here, we discuss some curvature properties on Sasakian manifold admitting *-Conformal η-Ricci soliton. We obtain some significant results on *-Conformal η-Ricci soliton in Sasakian manifolds satisfying R(ξ,X).S = 0, S(ξ,X).R = 0, {\overline}P(ξ,X…
The study finds conditions for Sasakian manifolds and generalised Ricci solitons.
problem Conditions for Sasakian manifolds and generalised Ricci solitons.
method Finding necessary conditions for both Sasakian structures and generalised Ricci solitons on odd-dimensional manifolds.
result Necessary conditions for both Sasakian structures and generalised Ricci solitons on odd-dimensional 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…
New proof classifies homogeneous 3-Sasakian and quaternionic Kähler manifolds.
problem Classifying homogeneous 3-Sasakian and quaternionic Kähler manifolds.
method Constructing an explicit one-to-one correspondence via root systems and analyzing properties of real projective spaces.
result Derivation of the classification of homogeneous positive quaternionic Kähler manifolds.
The article defines and analyzes Clairaut anti-invariant maps between Riemannian and trans-Sasakian manifolds.
problem Characterizing Clairaut anti-invariant Riemannian maps between specific types of manifolds.
method Deriving conditions for Clairaut maps, discussing integrability, and establishing harmonicity.
result Necessary and sufficient conditions for Clairaut anti-invariant maps are derived.
New method constructs degenerate Sasakian manifolds from hyperkähler bundles.
problem Constructing degenerate 3-(α,δ)-Sasakian manifolds. method Using fiber products of Boothby-Wang bundles over hyperkähler manifolds.
result No non-trivial compact examples exist, and one family of nilpotent Lie groups with this geometry is identified.
The Wu-Yau theorem is proven for Sasakian manifolds with specific curvature conditions.
problem Proving properties of Sasakian manifolds with negative transverse holomorphic sectional curvature.
method Analyzing the curvature properties and applying the Wu-Yau theorem.
result Compact Sasakian manifolds with negative transverse holomorphic sectional curvature have negative transverse Ricci curvature.
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.
Sasakian manifolds are odd-dimensional counterpart to Kahler manifolds. They can be defined as contact manifolds equipped with an invariant Kahler structure on their symplectic cone. The quotient of this cone by the homothety action is a complex manifold called Vaisman. We study harmonic forms and Hodge decomposition o…
Einstein like (ε)-para Sasakian manifolds are introduced. For an (ε)-para Sasakian manifold to be Einstein like, a necessary and sufficient condition in terms of its curvature tensor is obtained. The scalar curvature of an Einstein like (ε)-para Sasakian manifold is obtained and it…