The paper defines a new connection on sub-Riemannian manifolds and explores conditions for almost quasi-Sasakian manifolds to be Einstein.
problem Exploring new connections and conditions for specific types of manifolds.
method Defining a skew-symmetric connection and studying its properties on sub-Riemannian manifolds, and examining conditions for almost quasi-Sasakian manifolds to be Einstein.
result Sufficient conditions are found for an almost quasi-Sasakian manifold to be an Einstein manifold.
New class of manifolds studied with special properties.
problem Characterizing and studying a new class of almost contact metric manifolds.
method Introducing anti-quasi-Sasakian manifolds and analyzing their properties.
result Anti-quasi-Sasakian manifolds with constant curvature are flat and cokähler.
We provide models that are as close as possible to being formal for a large class of compact manifolds that admit a transversely Kaehler structure, including Vaisman and quasi-Sasakian manifolds. As an application we are able to classify the corresponding nilmanifolds.
3-quasi-Sasakian manifolds were recently studied by the authors as a suitable setting unifying 3-Sasakian and 3-cosymplectic geometries. In this paper some geometric properties of this class of almost 3-contact metric manifolds are briefly reviewed, with an emphasis on those more related to physical applications.
The article investigates almost Riemann solitons and gradient almost Riemann solitons in a specific type of manifold.
problem Investigating almost Riemann solitons and gradient almost Riemann solitons in a non-cosymplectic normal almost contact metric manifold.
method Analyzing properties of the manifold and its metrics under specific conditions.
result Established conditions under which almost Riemann solitons and gradient almost Riemann solitons reduce to known types of solitons or have specific properties.
Study of contact-complex Riemannian submersions in various manifold classes.
problem Characterizing submersions in specific manifold classes.
method Analyzing properties of O'Neill invariants and discussing integrability and minimality.
result Main properties of O'Neill invariants and integrability/minimality of fibres discussed.
In the present paper we carry on a systematic study of 3-quasi-Sasakian manifolds. In particular we prove that the three Reeb vector fields generate an involutive distribution determining a canonical totally geodesic and Riemannian foliation. Locally, the leaves of this foliation turn out to be Lie groups: either the o…
We classify locally homogeneous quasi-Sasakian manifolds in dimension five that admit a parallel spinor ψ of algebraic type F⋅ψ=0 with respect to the unique connection ∇ preserving the quasi-Sasakian structure and with totally skew-symmetric torsion. We introduce a certain conformal transformation of …
A structure on an almost contact metric manifold is defined as a generalization of well-known cases: Sasakian, quasi-Sasakian, Kenmotsu and cosymplectic. Then we consider a semi-invariant ξ⊥-submanifold of a manifold endowed with such a structure and two topics are studied: the integrability of distributions de…
Study on a specific type of Lie algebras with Kähler and contact properties.
problem Characterizing and classifying transversely Kähler almost contact metric Lie algebras.
method Analyzing properties of Lie algebras with contact forms and Kähler structures, considering center dimensions and quotient properties.
result Classification of 5-dimensional η-Einstein transversely Kähler almost contact metric Lie algebras.
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 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.
Study on invariant anti-quasi-Sasakian structures on compact manifolds.
problem Existence and classification of invariant anti-quasi-Sasakian structures of maximal rank.
method Analysis of invariant structures on compact homogeneous Riemannian manifolds and nilpotent Lie groups.
result Classification of invariant anti-quasi-Sasakian structures on nilpotent Lie groups.
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.
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.
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…
In the paper we introduce new metric structures on g-foliations that are less rigid than the well-known structures: almost contact and 3-quasi-Sasakian structures as well as f-structures with parallelizable kernel and almost para-φ-structures with complemented frames. We discuss the properties of the n…
We present a new method for classifying naturally reductive homogeneous spaces -- i.\,e.~homogeneous Riemannian manifolds admitting a metric connection with skew torsion that has parallel torsion \emph{and} curvature. This method is based on a deeper understanding of the holonomy algebra of connections with parallel sk…
The present paper deals with the study of Chaki-pseudo parallel and Deszcz-pseudo parallel invariant submanifolds of SQ-Sasakian manifolds with respect to Levi-Civita connection and semisymmetric metric connection and obtain that these two classes are equivalent with a certain condition. Also the invariant and anti-inv…
In this paper we prove a useful formula for the graded commutator of the Hodge codifferential with the left wedge multiplication by a fixed p-form acting on the de Rham algebra of a Riemannian manifold. Our formula generalizes a formula stated by Samuel I. Goldberg for the case of 1-forms. As first examples of applic…
The study examines Riemann solitons and almost solitons on specific Kenmotsu manifolds.
problem Characterizing solitons on Kenmotsu manifolds.
method Analysis of Riemann solitons and gradient almost Riemann solitons on almost Kenmotsu manifolds.
result Construction of examples of Kenmotsu and (κ,μ)′-almost Kenmotsu manifolds. The study classifies h-almost Ricci-Yamabe solitons in various paracontact manifolds.
problem Classifying h-almost Ricci-Yamabe solitons in paracontact geometry.
method Characterization and classification of para-Kenmotsu, para-Sasakian, and para-cosymplectic manifolds.
result Characterizations and classifications of various paracontact manifolds.
The paper defines and constructs almost complex blow-ups on 4D almost complex manifolds.
problem Existence and uniqueness of almost complex blow-ups on almost complex manifolds.
method Definition and construction of almost complex blow-ups, proving their existence and uniqueness.
result Existence and uniqueness of almost complex blow-ups on 4D almost complex manifolds.
Conditions for Penrose-Ward transformation on specific manifolds.
problem Conditions for Penrose-Ward transformation on almost G2-manifolds with almost twistorial structures. method Necessary and sufficient conditions derived through Penrose-Ward transformation.
result Conditions for Penrose-Ward transformation on almost G2-manifolds with almost twistorial structures. Almost para-Hermitian manifold it is manifold equipped with almost para-complex structure and compatible pseudo-metric of neutral signature. It is considered a class of immersions of almost para-Hermitian manifolds into almost para-Hermitian manifolds. Such immersions are called slant submanifolds. The concept is an an…
This paper is a study of almost contact statistical manifolds. Especially this study is focused on almost cosymplectic statistical manifolds. We obtained basic properties of such manifolds. It is proved a characterization theorem and a corollary for the almost cosymplectic statistical manifold with Kaehler leaves. We a…
Study connects Lie groups to specific Riemannian manifolds.
problem Understanding Lie groups through Riemannian manifold properties.
method Investigates Lie groups as 3D almost paracontact almost paracomplex Riemannian manifolds.
result Established correspondence between Lie algebra and matrix representation.
In this paper, by using the Bochner technique on almost Hermitian manifolds, we obtain a complex Hessian comparison for almost Hermitian manifolds generalizing the Laplacian comparison for almost Hermitian manifolds by Tossati, and reprove a diameter estimate for almost Hermitian manifolds by Gray. Moreover, we obtain …
In this article we study an almost f-cosymplectic manifold admitting a Ricci soliton. We first prove that there do not exist Ricci solitons on an almost cosymplectic (κ,μ)-manifold. Further, we consider an almost f-cosymplectic manifold admitting a Ricci soliton whose potential vector field is the Reeb vector fie…
Study on Hodge theory for almost complex manifolds.
problem Determining Hodge numbers for almost complex manifolds.
method Review and analysis of recent developments in Hodge theory for almost complex manifolds.
result Hodge numbers are almost complex, almost Kähler, or birational invariants in dimension four.
The paper defines η-normality for contact and paracontact manifolds and explores their properties.
problem Defining and characterizing η-normality for contact and paracontact manifolds. method Using the Levi-Civita covariant derivative and Tanaka-like connections.
result Existence and uniqueness of connections on η-normal manifolds. In this paper, we study the invariant and noninvariant hypersurfaces of (1,1,1) almost contact manifolds, Lorentzian almost paracontact manifolds and Lorentzian para-Sasakian manifolds, respectively. We show that a noninvariant hypersurface of an (1,1,1) almost contact manifold admits an almost product structure. We in…
Characterizes a class of almost Hermitian 4-manifolds using integral identities.
problem Global characterization of almost Hermitian 4-manifolds.
method Using an integral identity from Sekigawa's work, proving a uniqueness result on Lie algebras.
result Global characterization of the class AH1 of almost Hermitian 4-manifolds. It is introduced a differentiable manifold with almost contact 3-structure which consists of an almost contact metric structure and two almost contact B-metric structures. The product of this manifold and a real line is an almost hypercomplex manifold with Hermitian-Norden metrics. It is proven that the introduced mani…
Proves almost flat manifolds with mixed curvature bounds.
problem Finding structures with mixed curvature bounds.
method Mixed curvature analogue of Gromov's almost flat manifolds theorem.
result Proves upper and lower curvature bounds for almost flat manifolds.
Study local commutation relation on almost complex manifolds.
problem Local commutation relation between Lefschetz operator and exterior differential.
method Analyzing almost complex manifolds with compatible metrics.
result Generalizes local Kähler identities to almost Hermitian manifolds.
The canonical connection on a Riemannian almost product manifold is an analogue to the Hermitian connection on an almost Hermitian manifold. In this paper we consider the canonical connection on a class of Riemannian almost product manifolds with non-integrable almost product structure. We construct and characterize an…
New flow preserves almost Hermitian metrics for manifold study.
problem Curvature flow for almost Hermitian manifolds.
method Introducing a new curvature flow matching Ricci flow and preserving almost Hermitian condition.
result Ricci flow can be used to study almost Hermitian manifolds.
The study characterizes almost Kenmotsu manifolds with specific vector fields.
problem Characterizing almost Kenmotsu manifolds with holomorphically planar conformal vector fields.
method Analyzing properties of vector fields and curvature conditions.
result Classification of almost Kenmotsu manifolds as Kenmotsu or having specific geometric properties.
Paper solves a metric-independent problem on almost Kähler 4-manifolds.
problem Find a metric-independent generalization of Bott-Chern and Aeppli numbers.
method Introduced a new approach to generalize Bott-Chern and Aeppli numbers.
result Found a solution valid on almost Kähler 4-manifolds.
Study on solitons in specific geometric manifolds, proving manifold properties and presenting examples.
problem Exploring solitons in almost coKähler and asymptotically harmonic manifolds.
method Analyzing η-Einstein and gradient η-Einstein solitons in various geometric frameworks. result Proves manifold properties and presents examples validating results.
Classifies self-dual almost-Kähler 4-manifolds, proving uniqueness up to rescaling.
problem Classifying self-dual almost-Kähler four-manifolds.
method Using LeBrun's result and properties of Ricci tensor, the authors classify manifolds of different types.
result Any self-dual almost-Kähler metric on CP2 is the Fubini-Study metric up to rescaling. The study finds conditions for almost-Kähler 4-manifolds to be Kähler.
problem Conditions for almost-Kähler 4-manifolds to be Kähler.
method Analyzes harmonic self-dual Weyl curvature and constant scalar curvature.
result Compact almost-Kähler 4-manifolds with harmonic self-dual Weyl curvature and constant scalar curvature are Kähler if c1⋅ω≥0. The author is planning if possible classify all three-dimensional (κ,μ)-manifolds wether contact metric, almost cosymplectic, para-contact metric, almost para-cosymplectic. Of course classification in contact or almost cosymplectic cases already is provdied. Up to authors knowledge there is no classification for para…
Study on hyperspheres in 4-spaces as special Riemannian manifolds.
problem Characterizing hyperspheres in Euclidean and Minkowski 4-spaces as specific Riemannian manifolds.
method Constructing and studying hyperspheres in 4-dimensional spaces (Euclidean and pseudo-Euclidean) as almost paracontact almost paracomplex Riemannian manifolds.
result Characterization and geometric properties of these manifolds.
Study characterizes Einstein manifolds in almost Ricci solitons.
problem Characterizing Einstein manifolds in almost Ricci solitons.
method Geometric dynamics and geometric analysis methods.
result Characterizes Einstein manifolds in the class of complete almost Ricci solitons.
This paper is a complete study of almost α-paracosmplectic manifolds. We characterize almost α-paracosmplectic manifolds which have para Kaehler leaves. Main curvature identities which are fulfilled by any almost α-paracosmplectic manifold are found. We also proved that ξ is a harmonic vector field if and only if it is…
The study explores δ-almost gradient Yamabe solitons on pseudo-Riemannian manifolds.
problem Characterizing δ-almost gradient Yamabe solitons on pseudo-Riemannian manifolds.
method Analyzing δ-almost Yamabe solitons within the framework of para-contact metric manifolds, proving properties and conditions for solitons.
result Characterization of δ-almost gradient Yamabe solitons on K-paracontact metric manifolds.