The paper shows non-aspherical path components in G2-moduli spaces.
problem Characterizing non-aspherical path components in G2-moduli spaces.
method Using generalised Kummer construction and resolving singularities with Eguchi-Hanson spaces, the authors establish a fibration over each path component with Eilenberg Mac Lane spaces as fibres.
result The comparison map is a fibration over each path component with Eilenberg Mac Lane spaces as fibres, indicating non-trivial families of G2-manifolds.
The Borel Conjecture predicts that closed aspherical manifolds are topological rigid. We want to investigate when a non-aspherical oriented connected closed manifold M is topological rigid in the following sense. If f: N --> M is an orientation preserving homotopy equivalence with a closed oriented manifold as target, …
The Gauss-Bonnet inequality holds for certain non-aspherical manifolds up to dimension five.
problem Proving the Gauss-Bonnet inequality for non-aspherical manifolds.
method Analyzing the universal covering space and scalar curvature properties.
result The Gauss-Bonnet quantity is bounded and equality implies specific geometric structures.
Non-asphericity of strata of genus-one differentials
problem Strata of genus-one differentials
method Non-asphericity
result Infinitely many counterexamples to conjectures
We obtain restrictions on the topology of a closed connected manifold B that bounds a (possibly noncompact) manifold whose interior V admits a complete Riemannian metric of nonpositive sectional curvature. If G denotes the fundamental group of B, then a sample result is that B must be aspherical and incompressible if o…
We classify all closed, aspherical Riemannian manifolds M whose universal cover has indiscrete isometry group. One sample application is the theorem that any such M with word-hyperbolic fundamental group must be isometric to a negatively curved, locally symmetric manifold. Another application is the classification of a…
Proves 3D Poincaré duality groups without property (T)
problem Residually finite 3D Poincaré duality groups and property (T)
method Using coboundary expansion and recent results on 3-manifold groups
result 3D Poincaré duality groups without property (T)
In this paper we analyze the long-time behaviour of 3 dimensional Ricci flow with surgery. We prove that under the topological condition that the initial manifold only has non-aspherical or hyperbolic components in its geometric decomposition, there are only finitely many surgeries and the curvature is bounded by $C t^…
New flag-no-square 4-manifolds discovered with unique triangulations.
problem Identifying 4-manifolds with specific triangulation properties.
method Introduced star-connected-sum operation to preserve flag-no-square property; derived new constructions.
result Found non-aspherical flag-no-square 4-manifolds, answering a question by Przytycki and Swiatkowski.
New example shows noncontractible fiberings for a 3-manifold.
problem Understanding fiberings of S1imesS2. method Examining specific 3-manifolds and their fiber spaces.
result Components of SF(S1imesS2) are homotopy equivalent to ΩSO(3) and have noncontractible properties. Existence of harmonic maps from higher-dimensional manifolds to spheres proven.
problem Proving existence of nonconstant harmonic maps from arbitrary manifolds to spheres.
method Using optimal regularity and eigenvalue optimization on manifolds.
result First general existence result for harmonic maps from higher-dimensional manifolds to a large class of positively curved targets.
Extends Tian theorem to Vaisman manifolds for approximations.
problem Approximating Vaisman metrics by immersions/embeddings.
method Study Vaisman metrics on compact manifolds.
result Extend Tian's theorem to Vaisman manifolds.
In 1972, K. Kenmotsu studied a class of almost contact Riemannian manifolds. Later, such a manifold was called a Kenmotsu manifold. This paper, we studied Kenmotsu manifolds with (2n+s)-dimensional s−contact metric manifold and this manifold, we have called generalized Kenmotsu manifolds. Necessary and sufficient c…
Study on a new type of manifolds that generalize almost C-manifolds.
problem Understanding weak nearly C-manifolds and their properties.
method Analyzing conditions for local Riemannian product structures and characterizing specific dimensions.
result Conditions for a weak nearly C-manifold to become locally a Riemannian product and characterization of specific dimensions.
Stabilized convex symplectic manifolds are equivalent to flexible Weinstein manifolds.
problem Understanding the equivalence between stabilized convex symplectic manifolds and flexible Weinstein manifolds.
method Analyzing the homotopy type and symplectic properties of the manifolds.
result Stabilized convex symplectic manifolds are symplectomorphic to flexible Weinstein manifolds.
New class of complex manifolds defined, properties studied.
problem Understanding properties of complex manifolds.
method Introduced and studied wHHR manifolds, proved metric equivalence.
result Bergman and Kobayashi metrics are biLipschitz equivalent for wHHR Stein manifolds.
A selfsimiar manifold is a Riemannian manifold (M,g) endowed with a homothetic vector field ξ. We characterize global selfsimilar manifolds and describe the structure of local selfsimilar manifolds. We prove that any selfsimilar manifold with a potential homothetic vector field is a conical Riemannian ma…
Smoothly embed 3-manifolds in 5-manifolds, simplifying topological to smooth.
problem Embedding 3-manifolds smoothly in 5-manifolds.
method Homotopy and small homotopy to achieve smooth embeddings.
result Locally flat embeddings are homotopic to smooth ones.
The study provides a structure theorem for a new class of noncompact 3-manifolds.
problem Understanding a new class of noncompact 3-manifolds.
method Proved a structure theorem for irreducible open graph manifolds.
result A canonical 'reduced' decomposition of irreducible open graph manifolds along embedded, incompressible 2-tori.
Condition for intersection of real flag manifolds in complex flag manifold.
problem Intersection conditions of real flag manifolds in a complex flag manifold.
method Condition given in terms of symmetric triad, antipodal intersection proven.
result Intersection of real flag manifolds is antipodal.
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.
Conditions for flat manifolds as cusp cross-sections in arithmetic hyperbolic manifolds.
problem Determining when a flat manifold can be a cusp cross-section in arithmetic hyperbolic manifolds.
method Analyzing rational representations of holonomy groups and quasi-arithmetic manifolds.
result Conditions for a flat manifold to appear as a cusp cross-section in every commensurability class of arithmetic hyperbolic manifolds.
Classifies 3-manifolds from simplified (2,0)-trisections of 4-manifolds.
problem Classifying 3-manifolds from simplified (2,0)-trisections of 4-manifolds.
method Classifies vertical 3-manifolds as preimages of arcs on the plane for simplified (2,0)-trisection maps.
result Each 6-tuple of vertical 3-manifolds determines the source 4-manifold uniquely up to orientation reversing diffeomorphisms.
Study on 3D manifolds with specific tensor structures and their properties.
problem Characterizing 3D Riemannian manifolds with tensor structures.
method Investigation of locally conformal Riemannian product manifolds and their associated structures.
result Conditions for additional structures to be parallel and properties of almost Einstein and Einstein manifolds.
New manifold type PNDP-manifold defined with Einstein warped product structure.
problem Defining manifolds with non-standard dimensions.
method Einstein warped product manifold with special base and fiber structures.
result PNDP-manifolds are Einstein warped product manifolds with specific base and fiber properties.
Optimal inequalities for systole, inradius, and volume in hyperbolic 3-manifolds
problem Establishing optimal inequalities relating systole, inradius, and volume in hyperbolic 3-manifolds
method Using systole-volume inequalities for extremal manifolds
result Extremal manifolds for systole, inradius, and volume are identified
The paper explores F-manifolds and metrics, constructing canonical structures.
problem Understanding relationships between F-manifolds and metrics.
method Construction of canonical flat F-manifolds and homogeneous Riemannian F-manifolds.
result Construction of a canonical flat F-manifold associated to an arbitrary Riemannian F-manifold.
Defines s-manifolds and s-manifolds with corners for symplectic applications.
problem Creating a framework for singular manifolds with useful properties.
method Introducing categories of stratified manifolds and manifolds with corners.
result Fundamental classes and transverse fibre products in s-manifolds.
Embeds 3-manifolds in symplectic 4-manifolds with constraints.
problem Embedding 3-manifolds in symplectic 4-manifolds with topological and smooth properties.
method Topological and smooth embeddings, using homology cobordism and obstructions.
result 3-manifolds can be embedded in symplectic 4-manifolds with specific conditions.
We introduce a new general class of metric f-manifolds which we call (nearly) trans-S-manifolds and includes S- manifolds, C-manifolds, s-th Sasakian manifolds and generalized Kenmotsu manifold studied previously. We prove their main properties and we present many examples which justify their study.
The study provides homological characterizations for Q-manifolds and l2-manifolds.
problem Density of maps in characterizing Q-manifolds and l2-manifolds. method Investigates weakening the density of Zn-maps and Z-maps to homological maps. result Obtains homological characterizations for Q-manifolds and l2-manifolds. A locally conformally Kähler (LCK) manifold M is one which is covered by a Kähler manifold M~ with the deck transform group acting conformally on M~. If M admits a holomorphic flow, acting on M~ conformally, it is called a Vaisman manifold. Neither the class of LCK manifolds nor that of Vais…
Study weak quasi contact metric manifolds to generalize K-contact and Sasakian manifolds criteria.
problem Generalize K-contact and Sasakian manifolds criteria using weak quasi contact metric manifolds.
method Study weak quasi contact metric manifolds and generalize theorems for K-contact and Sasakian manifolds.
result Provide new criterions for K-contact and Sasakian manifolds in terms of curvature tensor and geometric objects.
The study classifies Kähler-Frobenius manifolds and their properties.
problem Classifying Kähler-Frobenius manifolds and understanding their structure.
method Using Topological Quantum Field Theory and Frobenius manifold theory.
result All flat compact Kähler manifolds are Frobenius manifolds and are classified.
Products of LCK manifolds do not admit LCK structures.
problem Whether products of compact complex manifolds admit LCK metrics.
method Classifying known LCK manifolds and proving non-existence of LCK structures in product cases.
result Products of LCK manifolds do not admit LCK structures.
Study geodesics on infinite-dimensional manifolds using Finsler structures.
problem Geodesics on Fréchet manifolds of Riemannian metrics.
method Establish Riemann-Finsler structures, prove existence and minimality of geodesics, derive Euler-Lagrange equations.
result Geodesics on Fréchet manifolds of Riemannian metrics are length minimizing and satisfy Euler-Lagrange equations.
New proof shows compact homogeneous LCK manifolds are Vaisman.
problem Proving compact homogeneous LCK manifolds are Vaisman.
method Using homogeneous LCK manifolds with potential and a new metric construction.
result Compact homogeneous LCK manifolds are Vaisman.
Paper proves existence of minimal surfaces in hyperbolic 3-manifolds.
problem Existence of minimal surfaces in non-compact 3-manifolds.
method Analyzes specific cases of hyperbolic 3-manifolds with bounded geometry and rank-1 cusps.
result Proves existence of minimal surfaces in various hyperbolic 3-manifolds.
A universal branched 3-manifold W characterizes Sol 3-manifolds.
problem Characterizing Sol 3-manifolds
method Using a universal branched 3-manifold W and a regular language result A closed 3-manifold M immerses into W if and only if M admits a Sol structure. The paper proves Liouville theorems for holomorphic maps on pseudo-Hermitian manifolds.
problem Proving Liouville theorems for holomorphic maps on pseudo-Hermitian manifolds.
method Analyzing maps between different classes of pseudo-Hermitian manifolds, using curvature assumptions.
result Holomorphic maps are constant under certain curvature conditions.
Proves almost flat spin^c manifolds bound compact manifolds.
problem Proving almost flat spin^c manifolds bound compact manifolds.
method Long-standing conjecture of Farrell--Zdravkovska and S. T. Yau settled.
result Every almost flat spin^c manifold bounds a compact orientable manifold.
The paper characterizes graph manifolds using fold maps and embeddability of polyhedra.
problem Understanding the global topologies of graph manifolds.
method Using fold maps into the plane and embeddability of polyhedra in 3-manifolds.
result Characterizes graph manifolds via fold maps and polyhedra embeddability.
The paper defines quasi-isometry for almost contact metric manifolds and explores its properties.
problem Understanding quasi-isometry in almost contact metric manifolds.
method Definition and study of quasi-isometry for almost contact metric manifolds.
result Established a relation between scalar curvature and quasi-isometric constants.
The study identifies flat manifolds with unique cusp cross-sections in arithmetic hyperbolic manifolds.
problem Characterizing flat manifolds that have unique cusp cross-sections in arithmetic hyperbolic manifolds.
method Algebraic characterization of cusp cross-sections in arithmetic hyperbolic manifolds.
result Construction of flat manifolds with unique cusp cross-sections and proof of their existence in all dimensions n≥32. 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 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…
Study classifies 3D Hessian manifolds, proving their topology.
problem Global topology of 3D Hessian manifolds.
method Proved structure and analyzed Betti numbers.
result Complete topological classification of 3D Hessian manifolds.
An (flat) affine 3-manifold is a 3-manifold with an atlas of charts to an affine space R3 with transition maps in the affine transformation group Aff(R3). Equivalently an affine 3-manifold is a 3-manifold with a flat torsion-free affine connection. We show that a closed affine 3-mani…