New criteria for Sasakian manifolds and classification of nearly cosymplectic manifolds.
problem Characterizing Sasakian and cosymplectic manifolds.
method Analyzing nearly Sasakian and nearly cosymplectic manifolds of dimensions greater than five.
result Every nearly Sasakian manifold of dimension greater than five is Sasakian.
New proof confirms nearly Sasakian condition for high-dimensional manifolds.
problem Characterizing Sasakian manifolds among almost contact metric manifolds.
method Self-contained, conceptual proof for nearly Sasakian condition.
result An almost contact metric manifold is Sasakian if and only if it is nearly Sasakian.
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…
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.
Study new CR-lightlike submanifolds in indefinite nearly Sasakian manifolds.
problem Characterizing new CR-lightlike submanifolds in indefinite nearly Sasakian manifolds.
method Introduce and study Quasi Generalized Cauchy-Riemann (QGCR) lightlike submanifolds.
result Derive necessary and sufficient conditions for integrability of distributions.
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.
Only the 6-sphere has constant curvature hypersurfaces in nearly Kähler manifolds.
problem Characterizing hypersurfaces with constant curvature in six-dimensional nearly Kähler manifolds.
method Proving hypersurfaces are η-quasi umbilical in specific spaces, then using non-existence results. result Only the 6-sphere has constant curvature hypersurfaces in nearly Kähler manifolds.
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.
Authors study a new type of submanifolds in a specific type of manifold.
problem Exploring a new type of submanifolds in indefinite nearly μ-Sasakian manifold. method Prove existence theorem and classification theorems for minimal and co-screen quasi generalized CR-lightlike submanifolds.
result Existence and classification theorems for specific submanifolds.
In this expository article we discuss the relations between Sasakian geometry, reduced holonomy and supersymmetry. It is well known that the Riemannian manifolds other than the round spheres that admit real Killing spinors are precisely Sasaki-Einstein manifolds, 7-manifolds with a nearly parallel G2 structure, and nea…
SU(3)-structures found on quotients of 3-Sasakian manifolds.
problem Exploring SU(3)-structures on specific quotients of 3-Sasakian manifolds.
method Analyzing quasi-regular 3-Sasakian orbifolds and their quotients, computing torsion and providing nearly Kähler structures.
result SU(3)-structures and nearly Kähler structures found on quotients of 3-Sasakian manifolds.
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.
Nearly G2-structures are unstable under a modified G2-Laplacian co-flow.
problem Stability of nearly G2-structures under geometric flows. method Normalized modified G2-Laplacian co-flow. result Many nearly G2-structures are unstable, with the standard structure on the round 7-sphere being an unstable critical point. New class of metric f-manifolds introduced.
problem No specific problem stated; focuses on introducing new class.
method Definition and properties of new class of metric f-manifolds.
result Properties and examples of new class of metric f-manifolds.
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 paper, we study warped product submanifolds of nearly trans-Sasakian manifolds. The non-existence of the warped product semi-slant submanifolds of the type Nθ×fNT is shown, whereas some characterization and new geometric obstructions are obtained for the warped products of the type $N_T\times{_{f}…
First non-trivial examples of deformed G_2-instantons, distinguishing nearly parallel G_2-structures.
problem Distinguishing between nearly parallel G_2-structures and isometric G_2-structures.
method Provided first non-trivial examples of deformed G_2-instantons and studied their deformation theory.
result Found non-trivial deformed G_2-instantons with obstructed deformation theory and moduli spaces of different dimensions.
We investigate instantons on manifolds with Killing spinors and their cones. Examples of manifolds with Killing spinors include nearly Kaehler 6-manifolds, nearly parallel G_2-manifolds in dimension 7, Sasaki-Einstein manifolds, and 3-Sasakian manifolds. We construct a connection on the tangent bundle over these manifo…
The study constructs associative 3-folds in squashed 3-Sasakian manifolds.
problem Understanding associative submanifolds in squashed 3-Sasakian manifolds.
method Analyzes foliations and geodesic ruled associative 3-folds correspondence.
result Infinitely many topological types of non-trivial associative 3-folds constructed.
SU(3)-structures found on specific orbifold quotients.
problem Exploring SU(3)-structures on orbifold quotients of 3-Sasakian orbifolds.
method Analyzing quasi-regular 3-Sasakian orbifolds and their quotients, computing torsion and providing nearly Kähler structures.
result SU(3)-structures and nearly Kähler structures on orbifold quotients are found.
New formula extends Ricci endomorphism action on spinors, with applications in geometry.
problem New $ rac{1}{2}$-Ricci type formula for spinorial action.
method Introduces a generalized $ rac{1}{2}$-Ricci type formula for spinorial action of Ricci endomorphism.
result Provides new alternative proof of Schrödinger-Lichnerowicz formula and integrability conditions.
The paper studies geometries with parallel skew-symmetric torsion and their submersions.
problem Understanding geometries with parallel skew-symmetric torsion.
method Analyzing metric connections and submersions.
result Complete local classification of geometries with parallel skew-symmetric torsion in principal bundle cases.
Study calibrated geometry in hyperkähler cones and their related spaces.
problem Characterize submanifolds in hyperkähler cones and related spaces.
method Systematic study of calibrated geometry in hyperkähler cones, 3-Sasakian manifolds, and twistor spaces.
result Obtain new characterizations of complex Lagrangian and complex isotropic cones in hyperkähler cones.
Classifies G2-instantons on Aloff-Wallach spaces, distinguishing nearly parallel structures.
problem Classifying G2-instantons on Aloff-Wallach spaces. method Classification of invariant G2-instantons for homogeneous coclosed G2-structures. result Examples of irreducible G2-instantons merging into reducible and obstructed ones. 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.
The paper examines *-Ricci tensor properties on Sasakian manifolds.
problem Analyzing *-Ricci tensor on Sasakian manifolds.
method Examining φ-confomally flat and confomally flat *-η-Einstein Sasakian manifolds, *-Ricci symmetric condition, and *-Ricci soliton.
result Investigates properties of *-Ricci tensor on Sasakian manifolds.
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.
New solutions found for G2 system on squashed manifolds.
problem Finding solutions to the heterotic G2 system on squashed manifolds.
method Constructing families of solutions using squashed metrics on 7-sphere or Aloff-Wallach space.
result Obtained AdS3 solutions for most squashing parameters, excluding a specific case.
Extends holomorphic Cartan geometry to Sasakian manifolds.
problem No specific problem stated; extends geometry to new context.
method Extends holomorphic Cartan geometry to Sasakian manifolds.
result Investigated branched holomorphic Cartan geometries on Sasakian Calabi-Yau manifolds.
The study examines properties of quasi-Para-Sasakian manifolds and their curvature.
problem Investigating curvature properties of quasi-Para-Sasakian manifolds.
method Basic properties and general curvature identities of quasi-Para-Sasakian manifolds are derived.
result If a quasi-Para-Sasakian manifold has constant curvature, it must be non-positive, and under specific conditions, it can be paracosymplectic or obtained by a homothetic deformation of a para-Sasakian structure.
Study of *-Conformal η-Ricci soliton on Sasakian manifolds.
problem Characterizing *-Conformal η-Ricci soliton on Sasakian manifolds.
method Analyzing curvature properties and conditions for *-Conformal η-Ricci soliton on Sasakian manifolds.
result Obtained significant results on *-Conformal η-Ricci soliton in Sasakian manifolds under specific curvature 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.
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.
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 studies second variation for L-minimal submanifolds in pseudo-Sasakian manifolds.
problem Analyzing stability of L-minimal submanifolds in pseudo-Sasakian manifolds.
method Provides a second variation formula and applies it to Lorentzian-Sasakian manifolds.
result Relates L-stability of Legendrians in a Sasakian manifold to their stability in an associated Lorentzian-Sasakian structure.
The paper classifies Sasakian immersions into odd spheres and finds new examples.
problem Classifying Sasakian immersions into odd-dimensional spheres.
method Analyzing compact Sasakian manifolds and using classification theorems.
result Infinite families of compact Sasakian η-Einstein manifolds cannot be immersed into odd spheres. Paper classifies 3D conformally flat quasi-Para-Sasakian manifolds.
problem Characterizing 3D conformally flat quasi-Para-Sasakian manifolds.
method Provided necessary and sufficient conditions for conformal flatness and characterized manifolds with η=const.
result Characterization of 3D conformally flat quasi-Para-Sasakian manifolds with η=const.
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…
For any triple (Mn,g,∇) consisting of a Riemannian manifold and a metric connection with skew-symmetric torsion we introduce an elliptic, second order operator Ω acting on spinor fields. In case of a reductive space and its canonical connection our construction yields the Casimir operator of the isometry gr…
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.
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.
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 extends Higgs bundle theory to Sasakian manifolds.
problem No direct problem stated, but extends theory to new manifold types.
method Extends Donaldson-Corlette-Hitchin-Simpson correspondence to Sasakian manifolds.
result Establishes correspondence between Higgs bundles and flat connections on Sasakian manifolds.