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.
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.
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 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 on special null submanifolds in indefinite Sasakian manifolds.
problem Characterizing null submanifolds in indefinite Sasakian manifolds.
method Proving properties of screen conformal null submanifolds and defining a new class.
result Existence of contact screen conformal r-null submanifolds in indefinite Sasakian space forms. 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.
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.
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.
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…
New types of null hypersurfaces found in Sasakian space-forms.
problem Identifying new structures in Sasakian space-forms.
method Defined and analyzed contact screen conformal and umbilic null hypersurfaces.
result Proved these hypersurfaces exist in Sasakian space forms with specific 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…
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.
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.
The study explores the types of Sasakian structures within a Sasaki cone and their properties.
problem Understanding the types of Sasakian structures within a Sasaki cone.
method Analyzing the Sasaki cone's dimension and properties of Sasakian structures.
result The types of Sasakian structures within a Sasaki cone can be either all positive, all indefinite, or a mix of both.
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.
In this paper we introduce the concept of (ε)-almost paracontact manifolds, and in particular, of (ε)-para Sasakian manifolds. Several examples are presented. Some typical identities for curvature tensor and Ricci tensor of (ε)-para Sasakian manifolds are obtained. We prove that if a…
Study characterizes geometric properties of QGCR-null submanifolds in cosymplectic manifolds.
problem Characterizing geometric properties of QGCR-null submanifolds in cosymplectic manifolds.
method Characterization through totally umbilical and irrotational properties, and discussion of geodesity conditions.
result Characterizes geometric properties of ascreen QGCR-null 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.
We classify flat strict nearly Kähler manifolds with (necessarily) indefinite metric. Any such manifold is locally the product of a flat pseudo-Kähler factor of maximal dimension and a strict flat nearly Kähler manifold of split signature (2m,2m) with m≥3. Moreover, the geometry of the second factor is encoded i…
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.
Investigates nearly Kähler and parallel G2 manifolds using Hitchin functionals.
problem Stability analysis of nearly Kähler and parallel G2 manifolds.
method Gradient flow of Hitchin functionals, spectral decomposition of Hessians, Hitchin index.
result Hitchin index provides a lower bound for the Einstein co-index.
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}…
We give an overview of some recent results in hypersymplectic and para-quaternionic Kahler geometry, and introduce the notion of split three-Sasakian manifold. In particular, we discuss the twistor spaces and Swann bundles of para-quaternionic Kahler manifolds. These are used to classify examples with a fully homogeneo…
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.
Study lightlike submanifolds in indefinite statistical manifolds, finding conditions and curvature expressions.
problem Characterize lightlike submanifolds in indefinite statistical manifolds.
method Analyze conditions for lightlike submanifolds to be lightlike statistical submanifolds, derive statistical sectional curvature, and investigate induced statistical Ricci tensor symmetry.
result Conditions for lightlike submanifolds to be lightlike statistical submanifolds and expressions for statistical sectional curvature and induced Ricci tensor symmetry.
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. We present a compared analysis of some properties of indefinite almost S-manifolds and indefinite S-manifolds. We give some characterizations in terms of the Levi-Civita connection and of the characteristic vector fields. We study the sectional and φ-sectional curvature of indefinite almost $\…
An η-Einstein condition is introduced in the context of indefinite g.f.f-manifolds, and a few Schur-type lemmas for indefinite S-manifolds are provided.
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 SASI-lightlike submanifolds in indefinite Kaehler manifolds.
problem Characterizing and understanding SASI-lightlike submanifolds in indefinite Kaehler manifolds.
method Introduced and analyzed SASI-lightlike submanifolds, derived conditions for metric connection, and investigated integrability of distributions.
result Found necessary and sufficient conditions for the induced connection to be a metric connection on SASI-lightlike submanifolds.
We study two types of isotropic planes: weakly isotropic and strongly isotropic planes. We prove that a Riemannian manifold of indefinite metric is conformally flat if and only if its curvature tensor vanishes on all the strongly isotropic planes. We specialize the plane axiom for Riemannian manifolds of indefinite met…
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.
We study the basic geometric properties of an indefinite locally conformal Kaehler 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.