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.
The paper introduces a statistical version of contact CR-product for Sasakian statistical manifolds.
problem Characterizing geometric properties of contact CR-submanifolds in Sasakian statistical manifolds.
method Characterization of integrability of invariant and anti-invariant distributions, development of results on specific types of contact CR submanifolds, introduction of statistical contact CR-product.
result Introduction of a statistical version of contact CR-product for Sasakian statistical manifolds.
Study geometric properties of SGL submanifolds in a specific manifold.
problem Analyzing geometric characteristics of SGL submanifolds.
method Examines integrability conditions and parallelism properties of distributions.
result Provides insights into geometric behavior of SGL submanifolds.
Paper introduces new hypersurface types on statistical manifolds.
problem Understanding new hypersurface types on statistical manifolds.
method Introducing and analyzing new classes of hypersurfaces.
result Obtained properties and relations on specific hypersurface types.
Statistical Lie algebras with constant curvature are linked to locally conformally Kähler structures.
problem Characterizing Lie algebras with constant curvature and their geometric implications.
method Constructing statistical manifolds and Sasakian structures to relate Lie algebras to locally conformally Kähler structures.
result Statistical Lie algebras of constant curvature correspond to locally conformally Kähler Lie algebras.
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.
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.
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.
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 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.
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.
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 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 study defines and explores properties of complex Sasakian manifolds.
problem Understanding the geometric structure of complex Sasakian manifolds.
method Definition and analysis of properties, curvature relations, and flatness conditions.
result Obtained useful curvature relations and examined flatness conditions for general curvature tensor B.
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.
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…
We extend the notion of (branched) holomorphic Cartan geometry on a complex manifold to the context of Sasakian manifolds. Branched holomorphic Cartan geometries on Sasakian Calabi-Yau manifolds are investigated.
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…
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.
In the present paper first, we define the conformal Sasakian manifolds and then we study geometry of invariant, anti-invariant and CR-submanifolds of conformal Sasakian manifolds.