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 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.
Study on CR-lightlike submanifolds in golden semi-Riemannian manifolds.
problem Exploring properties of CR-lightlike submanifolds in golden semi-Riemannian manifolds.
method Definition and investigation of properties of geodesic CR-submanifolds.
result Obtained results for totally geodesic and totally umbilical CR-submanifolds.
Introduces new lightlike submanifolds in indefinite Kaehler manifolds.
problem Characterizing and understanding new types of lightlike submanifolds.
method Definition and analysis of Screen Transversal Cauchy Riemann (STCR) lightlike submanifolds.
result Characterizes STCR lightlike submanifolds as umbrella of other types.
The paper studies extended quasi-Einstein manifolds with special geometric properties and solitons.
problem Exploring new types of manifolds in general relativity.
method Generalization of existing manifolds and construction of specific examples.
result Existence and properties of extended quasi-Einstein manifolds with solitons.
We introduce the notion of Poisson quasi-Nijenhuis manifolds generalizing the Poisson-Nijenhuis manifolds of Magri-Morosi. We also investigate the integration problem of Poisson quasi-Nijenhuis manifolds. In particular, we prove that, under some topological assumption, Poisson (quasi)-Nijenhuis manifolds are in one-one…
The paper examines properties of generalized τ-quasi Ricci-harmonic metrics and proves rigidity results.
problem Characterizing and proving rigidity of generalized τ-quasi Ricci-harmonic metrics.
method Exploring conditions for harmonic-Einstein metrics, obtaining rigidity results, and proving gap theorems.
result Rigidity results for compact generalized τ-quasi Ricci-harmonic metrics.
The paper introduces comprehensive quasi-Einstein spacetimes and explores their properties.
problem Exploring new types of spacetimes in general relativity.
method Mathematical analysis of geometric and physical properties of comprehensive quasi-Einstein manifolds.
result Existence of comprehensive quasi-Einstein spacetimes and their properties.
Study on generalized quasi-Einstein structures in contact geometry.
problem Characterizing and understanding generalized quasi-Einstein structures in contact geometry.
method Investigation of properties, existence, and characterizations of generalized quasi-Einstein normal metric contact pair manifolds.
result Normal metric contact pair manifolds with generalized quasi-constant curvature are generalized quasi-Einstein manifolds.
In this paper, we study the quasi-Einstein and generalized quasi-Einstein warped products with a semi-symmetric non-metric connection. We give the expressions of the Ricci tensors and scalar curvatures for the bases and fibres. In some cases we give some obstructions to the existence of the quasi-Einstein and generaliz…
Proves properties of generalized quasi Yamabe gradient solitons.
problem Characterize properties of generalized quasi Yamabe gradient solitons.
method Analyzes complete generalized quasi Yamabe gradient solitons and proves their properties.
result Proves that nontrivial complete generalized quasi Yamabe gradient solitons are quasi Yamabe gradient solitons on each component.
New structure found in loops on quasi-surfaces.
problem Understanding operations on loops in quasi-surfaces.
method Defined a quasi-Lie bialgebra structure.
result Natural operations on loops form a quasi-Lie bialgebra.
Paper introduces quasi-logconvex risk measures and their properties.
problem Characterizing and understanding new risk measures.
method Characterization through dual representation and properties of acceptance sets.
result Established dual representation and taxonomy of quasi-logconvex risk measures.
Proves symmetric spaces for certain quasi-isometric properties.
problem Understanding quasi-isometric spaces and their properties.
method Analyzes geometric and geometrically finite quasi-actions.
result Proves quasi-isometric spaces are symmetric or real line.
New Poisson structures defined on surface moduli spaces.
problem Generalizing Poisson brackets to quasi-surfaces.
method Defined quasi-Poisson brackets on quasi-surfaces.
result New Poisson structures on quasi-surfaces.
We propose a definition of Poisson quasi-Nijenhuis Lie algebroids as a natural generalization of Poisson quasi-Nijenhuis manifolds and show that any such Lie algebroid has an associated quasi-Lie bialgebroid. Therefore, also an associated Courant algebroid is obtained. We introduce the notion of a morphism of quasi-Lie…
Study proves positivity of quasi-local masses in general relativity using spinors.
problem Proving the positivity of quasi-local masses in general relativity.
method Using spinors and solving Dirac equation on compact Riemannian manifolds with boundary conditions.
result Gravitational mass bounded by a spacelike topological 2-sphere is non-negative, vanishing only in Minkowski space.
Study on quasi-statistical structures on manifolds and their properties.
problem Characterizing quasi-statistical structures and their integrability.
method Introducing generalized quasi-statistical structures and proving their integrability conditions.
result Any quasi-statistical structure on a manifold induces generalized quasi-statistical structures on its tangent and cotangent bundles.
The paper studies quasi-X-convex functions and their applications in optimization.
problem Optimization problems with quasi-X-convex functions. method Definition and study of X-convex, quasi-X-convex, and related functions. result Applications of quasi-X-convex functions in optimization problems. The paper introduces new Finsler metrics and associated weighted quasi-metrics.
problem Geometric properties of Finsler metrics and quasi-metric spaces.
method Construction of weighted quasi-metrics associated with Finsler metrics.
result Investigation of geometric properties of weighted quasi-metric spaces.
Study finds conditions for certain warped product manifolds to be quasi-Einstein.
problem Conditions for quasi-Einstein sequential warped product manifolds.
method Investigated necessary and sufficient conditions for specific types of manifolds.
result Identified conditions for sequential warped product manifolds to be quasi-Einstein.
Develops quasi-likelihood analysis for marked point processes and applies it to Hawkes processes.
problem Analyzing multivariate marked point processes and their applications.
method Quasi-likelihood analysis for a general class of multivariate marked point processes, with focus on marked Hawkes processes.
result The quasi-likelihood analysis for marked Hawkes processes provides explicit conditions for ergodicity and Markovian transformation.
Paper connects CNT and WY quasi-local energies, finding saddle points.
problem Connecting quasi-local energies and their properties.
method Analyzing second variations of CNT quasi-local energy for Kerr-like spacetimes.
result Second variation of CNT quasi-local energy is a saddle point in most cases.
Study classifies half conformally flat GQE manifolds of signature (2,2).
problem Classifying half conformally flat generalized quasi-Einstein manifolds.
method Analysis and examples provided.
result Natural affine quasi-Einstein equation derived.
This (quasi-)survey addresses the quasi-isometry classification of locally compact groups, with an emphasis on amenable hyperbolic locally compact groups. This encompasses the problem of quasi-isometry classification of homogeneous negatively curved manifolds. A main conjecture provides a general description; an extend…
The study characterizes mixed super quasi-Einstein manifolds with Ricci-Bourguignon solitons.
problem Characterizing mixed super quasi-Einstein manifolds with Ricci-Bourguignon solitons.
method Exploring properties of mixed super quasi-Einstein manifolds, including conformal Ricci pseudosymmetry and Einstein's field equation. Characterizing manifolds that admit Ricci-Bourguignon solitons and providing a detailed eigenvalue problem characterization.
result Characterization of mixed super quasi-Einstein manifolds with Ricci-Bourguignon solitons, including a detailed eigenvalue problem and an example construction.
Proof that specific groups are quasi-isometrically rigid.
problem Quasi-isometric rigidity of specific groups.
method Proof of quasi-isometric rigidity for Kleinian and three-manifold groups.
result Finitely generated Kleinian and three-manifold groups are quasi-isometrically rigid.
In this note, we announce the first results on quasi-isometric rigidity of non-nilpotent polycyclic groups. In particular, we prove that any group quasi-isometric to the three dimenionsional solvable Lie group Sol is virtually a lattice in Sol. We prove analogous results for groups quasi-isometric to R⋉Rn wh…
The paper analyzes symmetry groups of a specific type of manifold.
problem Understanding the symmetry groups of generalized m-quasi-Einstein manifolds. method Analyzing a n-dimensional generalized m-quasi-Einstein manifold conformal to a pseudo-Euclidean space. result Proves the most general symmetry group of maximal dimension and shows no different low-dimensional invariants.
This paper proves certain quasi-Einstein manifolds are rigid under Ricci flow.
problem Understanding the behavior of quasi-Einstein metrics under Ricci flow.
method Employing a curvature evolution identity associated with Ricci flow.
result Certain closed quasi-Einstein manifolds are rigid under Ricci flow.
Characterizes quasi-projective even Artin groups based on graph labels.
problem Understanding quasi-projective even Artin groups.
method Characterization through defining graph properties and K(pi,1) spaces.
result Quasi-projective even Artin groups are realizable by K(pi,1) quasi-projective spaces.
Proves a new Penrose inequality for static spacetimes.
problem Establishing a lower bound on mass using area and static references.
method Develops a new quasi-local Penrose inequality for spherically symmetric static spacetimes.
result Proves a quasi-local Penrose inequality for any spherically symmetric static spacetime.
Study on rigidity and characterization of generalized quasi-Einstein manifolds.
problem Rigidity and characterization of generalized quasi-Einstein manifolds.
method Analytical and geometric methods, including rigidity results and potential function analysis.
result Characterization of manifolds conformal to Euclidean space and explicit examples.
In this paper we introduce the notion of generalized quasi--Einstein manifold, that generalizes the concepts of Ricci soliton, Ricci almost soliton and quasi--Einstein manifolds. We prove that a complete generalized quasi--Einstein manifold with harmonic Weyl tensor and with zero radial Weyl curvature, is locally a war…
With any non necessarily orientable unpunctured marked surface (S,M) we associate a commutative algebra, called quasi-cluster algebra, equipped with a distinguished set of generators, called quasi-cluster variables, in bijection with the set of arcs and one-sided simple closed curves in (S,M). Quasi-cluster variables a…
Harmonic maps prove quasi-isometric embeddings are close to unique.
problem Understanding quasi-isometric embeddings between pinched Hadamard manifolds.
method Proving quasi-isometric maps are close to harmonic maps.
result Quasi-isometric maps are within bounded distance from a unique harmonic map.
Paper defines semi-quasi-Einstein manifolds and applies to Schwarzschild and Kottler spacetimes.
problem Defining and studying semi-quasi-Einstein manifolds.
method Introduced from a semi symmetric metric connection, analyzed with curvature conditions and Killing generators.
result Schwarzschild and Kottler spacetimes exhibit semi-quasi-Einstein structure.
We prove that PSL(2,Z[1/p]) gives the first example of groups which are not quasi-isometric to each other but have the same quasi-isometry group. Namely, PSL(2,Z[1/p]) and PSL(2,Z[1/q]) are not quasi-isometric unless p=q, and, independent of p, the quasi-isometry group of PSL(2,Z[1/p]) is PSL(2,Q). In addition, we char…
Study on link-homotopy of pretzel links using quasi-trivial quandles and biquandles.
problem Link-homotopy of pretzel links.
method Investigation of quasi-trivial quandles and biquandles, cocycle enhancements.
result Necessary and sufficient condition for pretzel links to be trivial under link-homotopy.
We say A is a quasi-normal subgroup of the group G if the commensurator of A in G is all of G. We develop geometric versions of commensurators in finitely generated groups. In particular, g is an element of the commensurator of A in G iff the Hausdorff distance between A and gA is finite. We show that a quasi-normal su…
We rigorously define the Liouville action functional for finitely generated, purely loxodromic quasi-Fuchsian group using homology and cohomology double complexes naturally associated with the group action. We prove that the classical action - the critical point of the Liouville action functional, considered as a funct…
Random walks generate quasi-convex subgroups in acylindrically hyperbolic groups.
problem Understanding the structure of subgroups generated by random walks in hyperbolic groups.
method Probabilistic approach using random walks in acylindrically hyperbolic groups.
result Subgroups generated by random walks are quasi-convex and isomorphic to the original subgroup and the random walk subgroup.
In this paper, we prove that certain spaces are not quasi-isometric to Cayley graphs of finitely generated groups. In particular, we answer a question of Woess and prove a conjecture of Diestel and Leader by showing that certain homogeneous graphs are not quasi-isometric to a Cayley graph of a finitely generated group.…
In this paper, for a Jacobi algebroid A, by introducing the notion of Jacobi quasi-Nijenhuis algebroids, which is a generalization of Poisson quasi-Nijenhuis manifolds introduced by Stiénon and Xu, we study generalized complex structures on the Courant-Jacobi algebroid A⊕A∗, which unifies generalized complex…
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.
The study confirms a conjecture about Kähler manifolds with quasi-negative curvature.
problem Confirming a long-standing conjecture about Kähler manifolds with quasi-negative curvature.
method Introducing (ε,δ)--quasi-negativity and applying gap-type theorems. result Obtained gap-type theorems for ∫Xc1(KX)n>0 in terms of real bisectional curvature and weighted orthogonal Ricci curvature. In this paper, we introduce the notion of Reidemeister torsion for quasi-isomorphisms of based chain complexes over a field. We call a chain map a quasi-isomorphism if its induced homomorphism between homology is an isomorphism. Our notion of torsion generalizes the torsion of acyclic based chain complexes, and is a ch…
Proves a generalized vanishing theorem for quasi-smooth stacks, with applications in K-theory and birational geometry.
problem Vanishing theorems for quasi-coherent sheaves on derived blow-ups of quasi-smooth stacks.
method Derived blow-ups, intrinsic blow-up theory, Kiem-Li-Savvas blow-up theory, virtual localization theorem, desingularization theorem, resolution of diagonal.
result Generalized vanishing theorem for quasi-coherent sheaves on derived blow-ups of quasi-smooth stacks.