The author aims to classify 3D (κ,μ)-manifolds, focusing on para-contact and almost para-cosymplectic cases.
problem Classifying 3D (κ,μ)-manifolds, especially para-contact and almost para-cosymplectic. method Analyzing and conjecturing about structures that provide classification.
result These 3D manifolds are fundamental building blocks for higher-dimensional 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.
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.
There are studied in details 5-dimensional pseudo-Riemannian manifolds equipped with the structure analogous to the almost cosymplectic (almost coKaehler) structure. The curvature by assumption commutes with the structure affinor and all these manifolds are Walker spaces. There are obtained classifications for manifold…
The paper classifies 3D paracontact and almost paracosymplectic spaces.
problem Classifying 3D paracontact and almost paracosymplectic spaces.
method Detailed structure analysis and local classification for all possible values of κ.
result Local classification of paracontact metric and almost paracosymplectic (κ,μ)-spaces for every possible value of κ.
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.
Harmonic almost complex structures on specific Lie groups and solvmanifolds identified.
problem Characterizing harmonic almost complex structures on almost abelian Lie groups and solvmanifolds.
method Adapted Gray-Hervella classification to almost abelian Lie groups, characterized harmonic structures.
result Examples of harmonic almost complex structures in different Gray-Hervella classes on compact almost abelian solvmanifolds.
Extends positive and almost positive links to successively almost positive ones.
problem Extending properties of positive and almost positive diagrams and links.
method Introducing successively almost positive diagrams and links, and analyzing their properties.
result Improves known results of positive and almost positive links.
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.
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. Study computes invariants on six-dimensional solvmanifolds, providing symplectic structure obstructions.
problem Computing invariants on six-dimensional solvmanifolds.
method Computed almost-complex and almost-Hermitian invariants on families of solvmanifolds.
result Provides obstructions to symplectic structures on compact 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. Abstract: Almost Kähler Hodge numbers vary with metric choices.
problem Variation of almost Kähler Hodge numbers with metrics.
method Analysis of almost complex Hodge numbers under different almost Kähler metrics.
result The almost Kähler Hodge number h0,1 varies with metric choices. 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.
Study of almost Yamabe solitons on Kaehler submersions.
problem Characterizing almost Yamabe solitons on Kaehler submersions.
method Analyzing conditions for solitons to be shrinking, steady, or expanding.
result Characterizations for almost Yamabe solitons in terms of extrinsic horizontal scalar curvature.
Study almost rigidity of super Ricci flow with non-negative Muller quantity.
problem Almost rigidity properties of super Ricci flow with non-negative Muller quantity.
method Almost splitting and quantitative stratification theorems established by Bamler for Ricci flow.
result Obtained almost constancy for a certain integral quantity concerning scalar curvature at an almost self-similar point.
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…
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.
Study shows almost complex structures with certain tensor properties are prevalent.
problem Characterizing almost complex structures with specific tensor properties.
method Analyzes the space of almost complex structures on compact manifolds.
result The space of almost complex structures with rank at least k Nijenhuis tensor is either empty or dense in each component.
In this paper we introduce the notion of almost flatness for (stably) relative bundles on a pair of topological spaces and investigate basic properties of it. First, we show that almost flatness of topological and smooth sense are equivalent. This provides a construction of an almost flat stably relative bundle by usin…
The notion of generalized almost paracontact structure on the generalized tangent bundle TM⊕T∗M is introduced and its properties are investigated. The case when the manifold M carries an almost paracontact metric structure is also discussed. Conditions for its transformed under a β- or a B-field transfor…
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.
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.
Study on biharmonic almost complex structures on compact manifolds.
problem Existence and regularity of biharmonic almost complex structures.
method Analyzes biharmonic almost complex structures on compact almost Hermitian manifolds, focusing on dimension four.
result Existence of energy-minimizing biharmonic almost complex structures for various topologies and homotopy classes.
Study various submanifolds in quaternionic skew-Hermitian spaces.
problem Characterize submanifolds in almost quaternionic skew-Hermitian manifolds.
method Construct explicit examples of submanifolds in semisimple quaternionic skew-Hermitian symmetric spaces.
result Explicit examples of submanifolds for each type considered.
In this paper, the notion of an almost contact Kählerian structure is introduced. The interior geometry of almost contact Kählerian spaces is investigated. On the zero-curvature distribution of an almost contact metric structure, as on the total space of a vector bundle, an almost contact Kählerian structure is obtaine…
In this article, we study an almost contact metric structure on a G2-manifold constructed by Arikan, Cho and Salur in via the classification of almost contact metric structures given by Chinea and Gonzalez. In particular, we characterize when this almost contact metric structure is cosymplectic and narrow down the p…
We show that any compact almost-complex manifold of complex dimension m can be pseudo-holomorphically embedded in R^(6m) equipped with a suitable almost-complex structure.
Solves a generalized Monge-Ampère equation on Kähler surfaces, proving a conjecture.
problem Existence and uniqueness of solutions to a generalized Monge-Ampère equation.
method Analyzes the equation's dependence on almost Kähler structure and proves Donaldson's conjecture.
result Proves Donaldson's conjecture for tamed almost complex 4-manifolds.
New research finds infinitely many hyperbolic knots not almost-fibered.
problem Understanding the properties of knots and their complements.
method Examined hyperbolic knots and their Seifert surfaces.
result Existence of infinitely many hyperbolic genus one knots that are not almost-fibered.
In this paper the notion of the intrinsic geometry of an almost contact metric manifold is introduced. Description of some classes of spaces with almost contact metric structures in terms of the intrinsic geometry is given. A new type of almost contact metric spaces, more precisely, Hermitian almost contact metric spac…
New structure with B-metric extends classical almost contact structures.
problem Extending classical almost contact structures with new geometric properties.
method Introduced and studied weak almost contact structures with B-metric.
result Several geometric properties and special classes are obtained.
Unique tangent cones found for boundary points of 2D almost-minimizing currents.
problem Characterizing boundary points of two-dimensional almost-minimizing currents.
method Combining epiperimetric inequality and almost-monotonicity formula.
result Tangent cones at singular boundary points are unique.
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…
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…
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…
Two constructions link path geometries to almost Grassmann structures.
problem Linking path geometries to almost Grassmann structures.
method Introducing two Fefferman-type constructions.
result Characterizing conditions for almost Grassmann structures arising from these constructions.
The paper explores families of almost complex structures and transverse (p,p)-forms.
problem Understanding and producing families of almost p-Kähler structures.
method Producing families of almost p-Kähler structures (Jt,Ωt) on $\C^3$, $\C^4$, and T6. result The almost complex structures Jt cannot be locally compatible with any symplectic form for teq0. A link is almost alternating if it is non-alternating and has a diagram that can be transformed into an alternating diagram via one crossing change. We give formulas for the first two and last two potential coefficients of the Jones polynomial of an almost alternating link. Using these formulas, we show that the Jones …
In this paper, motivated by Chen--Ruan's stringy orbifold theory on almost complex orbifolds, we construct a new cohomology ring HG,cs∗(X) for an equivariant almost complex pair (X,G), where X is a compact connected almost complex manifold, G is a connected compact Lie group which acts on X an…
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 study examines almost Ricci-Yamabe solitons on almost Kenmotsu manifolds and their properties.
problem Characterizing almost Ricci-Yamabe solitons on almost Kenmotsu manifolds.
method Analyzing the conditions for almost Ricci-Yamabe solitons to be η-Einstein and proving local isometry for certain manifolds.
result Properties of almost Ricci-Yamabe solitons on (2n+1)-dimensional (κ,μ)′-AKMs. The paper proves smoothness of weakly biharmonic almost complex structures in dimension four.
problem Existence and regularity of weakly polyharmonic almost complex structures.
method Elliptic system analysis and critical growth nonlinearities.
result Weakly biharmonic almost complex structures are smooth in dimension four.
We prove that any compact almost complex manifold (M,J) of real dimension 2m admits a pseudo-holomorphic embedding in a Euclidean space of dimension 4m+2, endowed with a suitable non-standard almost complex structure. Moreover, we give a necessary and sufficient condition, expressed in terms of the Segre class…
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 …
Study harmonicity of normal almost contact structures on Riemannian manifolds.
problem Understanding harmonicity of normal almost contact structures.
method Analyzing harmonicity through associated sections of a twistor bundle and rewriting equations in terms of curvature tensor.
result Conditions relating harmonicity of almost contact metric and almost complex structures.
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.