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. Characterizes separable subgroups in 3-manifold groups.
problem Identifying which subgroups of 3-manifold groups are separable.
method Complete characterization using spirality and torus decomposition.
result Characterization generalizes previous work on surface subgroups.
Characterizes specific harmonic manifolds using Laplacian eigenfunctions.
problem Characterizing harmonic manifolds.
method Using radial eigenfunctions of the Laplacian.
result Characterizes space forms, complex hyperbolic spaces, and quaternionic hyperbolic spaces as harmonic manifolds.
Characterizes CR manifolds as critical points of an energy functional.
problem Understanding homogeneous three-dimensional CR manifolds.
method Uses an energy functional dependent on Webster curvature and torsion.
result Identifies Rossi spheres as a specific type of critical point.
Characterizes conditions for quotient spaces of decompositions to be manifolds.
problem Conditions for quotient spaces of decompositions to be manifolds.
method Generalized characterizations of upper semi-continuity for decomposition into one for a class decomposition.
result Characterizations of necessary and sufficient conditions for quotient spaces of decompositions to be k-manifolds (k=1,2). 3-manifold triangulations are Golod and tight, proven through a topological characterization.
problem Understanding Golodness and tightness in 3-manifold triangulations.
method Topological characterization of a polyhedral product for a tight-neighborly manifold triangulation.
result Golodness and tightness are equivalent for 3-manifold triangulations.
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 study characterizes generalized Berwald surfaces with topological constraints.
problem Topological constraints on generalized Berwald surfaces.
method Intrinsic characterization and examples.
result Results on topological obstructions for the base manifold.
The paper characterizes warped product submanifolds in LCS-manifolds.
problem Characterizing warped product submanifolds in LCS-manifolds.
method Analyzing contact CR-warped product and pseudo-slant submanifolds, and constructing examples.
result There do not exist any proper warped product bi-slant submanifolds of LCS-manifolds.
Characterizes pseudo-collarable manifolds with noncompact boundaries.
problem Characterizing manifolds with noncompact boundaries.
method Extends earlier work by Guilbault and Tinsley to include noncompact boundaries, extending Siebenmann's work.
result Complete characterization of pseudo-collarable n-manifolds for n≥6. Study characterizes kernel of mixed ray transform on simple surfaces.
problem Characterizing the kernel of mixed ray transform on simple surfaces.
method Characterization of the kernel through analysis of mixed ray transform on simple 2D Riemannian manifolds.
result Characterization of the kernel of the mixed ray transform on simple surfaces.
Geodesic orbit Riemannian structures on R^n characterized.
problem Characterizing Riemannian manifolds with geodesic orbits.
method Geometric and algebraic characterization of geodesic orbit manifolds diffeomorphic to R^n.
result Established structural properties of geodesic orbit manifolds.
New characterizations for manifolds with boundary rigidity results.
problem Rigidity results for compact gradient Einstein-type manifolds with boundaries.
method Analyzing manifolds with rigidity results and characterizations.
result New topological and geometric characterizations for manifolds with boundaries.
Results on characterization of manifolds in terms of certain Lie algebras growing on them, especially Lie algebras of differential operators, are reviewed and extended. In particular, we prove that a smooth (real-analytic, Stein) manifold is characterized by the corresponding Lie algebra of linear differential operator…
Characterizes certain Kähler manifolds with doubly-warped product structures.
problem Understanding Kähler manifolds with specific geometric properties.
method Obata-type characterization for Kähler manifolds with doubly-warped product structures.
result Complete description of Kähler doubly-warped product structures with Einstein metrics.
The null energy condition is characterized via convexity of entropy in Lorentzian manifolds.
problem Characterizing the null energy condition in Lorentzian manifolds.
method Characterization via convexity of the relative entropy along displacement interpolations on null hypersurfaces.
result The null energy condition is characterized in terms of convexity of the relative entropy.
Characterizes connections on normal distributions manifold.
problem Geometric characterization of connections on normal distributions.
method Homogeneous statistical manifold structure and Lie group analysis.
result Geometric characterization of α-connections on Lie group. Abstract: Characterizes special Kähler manifolds with specific properties.
problem Characterizing Kähler manifolds with special properties.
method Analyzes properties of functions and gradients on manifolds.
result Characterizes manifolds supporting certain functions and gradients.
Spin-structures on real Bott manifolds with Kähler structure are characterized.
problem Existence of spin-structures on real Bott manifolds with Kähler structure.
method Ishida characterization and techniques from \cite{PS16} using characteristic classes.
result Necessary and sufficient condition for the existence of spin-structures on M. Paper characterizes tamed and weakened tamed four-manifolds using a new technique.
problem Characterizing tamed and weakened tamed four-manifolds.
method Using weakly \widetilde{\mathcal{D}}^+_J -closed technique.
result Characterization of tamed and weakened tamed four-manifolds.
GC Stein manifolds characterized with embeddings and functions.
problem Characterize GC Stein manifolds using embeddings and functions.
method Extended Cartan's Theorem A and B, defined L-plurisubharmonic functions, established GH embeddings. result Characterized GC Stein manifolds via L-plurisubharmonic exhaustion functions and GH embeddings. Characterizes Hermitian manifolds with Bismut parallel torsion.
problem Understanding curvature properties of Hermitian manifolds with specific torsion.
method Analyzes Bismut curvature tensor and parallel torsion conditions.
result Characterizes Bismut torsion parallel manifolds using Bismut curvature alone.
Characterizes Q-manifold bundles over C-spaces.
problem Homological characterization of Q-manifolds bundles. method Homological proof of Q-manifolds bundles over C-spaces. result Provides a partial answer to Question QM22.
The study characterizes locally φ-semisymmetric Kenmotsu manifolds.
problem Understanding the properties of Kenmotsu manifolds.
method Characterization through local φ-semisymmetry.
result Characterization of locally φ-semisymmetric Kenmotsu manifolds.
Characterizes and examines gradient solitons on doubly warped product manifolds.
problem Understanding gradient solitons on specific manifold structures.
method Characterizations and examinations of various types of gradient solitons on doubly warped product manifolds.
result Effects of gradient solitons on factor manifolds and specific curvature properties of doubly warped products.
Characterizes affine vector fields on Finsler manifolds with rigidity results.
problem Understanding affine vector fields on Finsler manifolds.
method Utilizing the Jacobi type equation and spray characterization, proving rigidity theorems.
result Rigidity theorems for affine vector fields on Finsler manifolds with non-positive total Ricci curvature.
Among all C∞-algebras we characterize those which are algebras of smooth functions on smooth separable Hausdorff manifolds.
New curvature condition helps characterize Kähler manifolds.
problem Characterize compact Kähler manifolds with specific curvature properties.
method Introduce and utilize 2−positive bisectional curvature condition. result Deduce characterization theorem for manifolds with 2−positive bisectional curvature. We derive some elliptic differential inequalities from the Weitzenböck formulas for the traceless Ricci tensor of a Kähler manifold with constant scalar curvature and the Bochner tensor of a Kähler-Einstein manifold respectively. Using elliptic estimates and maximum principle, some Lp and L∞ pinching result…
The study characterizes and classifies specific types of manifolds using conformal and quasi-Einstein properties.
problem Characterizing and classifying manifolds with specific geometric properties.
method Analyzing warped products, contact manifolds, and semi-Riemannian manifolds.
result Characterizations and classifications of weakly conformally flat and quasi-Einstein manifolds.
We develop a theory of Nobeling manifolds similar to the theory of Hilbert space manifolds. We show that it reflects the theory of Menger manifolds developed by M. Bestvina and is its counterpart in the realm of complete spaces. In particular, the Nobeling manifold characterization conjecture is proven.
We characterize the quasiprojective groups that appear as fundamental groups of compact 3-manifolds (with or without boundary). We also characterize all closed 3-manifolds that admit good complexifications. These answer questions of Friedl--Suciu, \cite{fs}, and Totaro \cite{tot}
Characterizes CR manifolds in complex flag manifolds.
problem Closed real orbits in complex flag manifolds.
method Characterization through CR manifold structures and real forms.
result Closed orbits are finitely nondegenerate.
The study characterizes symmetries in Kaehler manifolds.
problem Understanding symmetries in Kaehler manifolds.
method Analyzing specific types of Kaehler manifolds: constant holomorphic sectional curvature, semisymmetric, and holomorphically pseudosymmetric.
result Characterization results and geometric interpretation of the complex Tachibana tensor.
New characterizations of umbilic hypersurfaces in warped product manifolds.
problem Characterizing umbilic hypersurfaces in specific warped product manifolds.
method Using a new integral formula or Brendle's Heintze-Karcher type inequality.
result Generalizations of classical theorems in Euclidean space to warped product manifolds.
The paper characterizes submersions with Ricci soliton total manifolds and their properties.
problem Characterizing submersions with Ricci soliton total manifolds.
method Analyzing Riemannian submersions and their properties, focusing on fiber and target manifolds.
result Necessary conditions for the target manifold to be a Ricci soliton and characterizations of harmonicity.
New geometric approach to slow invariant manifolds in dynamical systems.
problem Characterizing slow invariant manifolds in a coordinate-independent manner.
method Exploiting curvature concepts and variational approach in Hamiltonian mechanics.
result Differential geometric definition of slow invariant manifolds proposed.
We give an algebraic characterization of the possible characteristic tensors of an infinitesimally homogeneous affine manifold with G-structure.
Study symmetric Killing 2-tensors on manifolds, focusing on Sasakian and Euclidean spheres.
problem Characterize symmetric Killing 2-tensors on Riemannian manifolds.
method Analyze conditions on symmetric Killing 2-tensors, focusing on Sasakian and Euclidean spheres.
result Recover characterization of spheres using functions satisfying a differential equation.
Characterizes rigidity of compact foliations using deformations of Lie groupoids and algebroids.
problem Rigidity of compact foliations on manifolds.
method Combining stability results for foliations with recent results on deformations of Lie groupoids and Lie algebroids.
result Cohomological characterization for rigidity of compact foliations.
We prove metric rigidity for complete manifolds supporting solutions of certain second order differential systems, thus extending classical works on a characterization of space-forms. In the route, we also discover new characterizations of space-forms. We next generalize results concerning metric rigidity via equations…
We calculate the intersection ring of three-dimensional graph manifolds with rational coefficients and give an algebraic characterization of these rings when the manifold's underlying graph is a tree. We are able to use this characterization to show that the intersection ring obstructs arbitrary three-manifolds from be…
Characterizes knots with L-space surgeries in 3-sphere and lens spaces.
problem Identifying knots with specific L-space surgeries.
method Characterization of (1,1) knots and braids in 3-sphere and lens spaces.
result Characterizes knots with non-trivial L-space surgeries.
The paper characterizes warped product manifolds under pseudosymmetric conditions.
problem Characterizing warped product manifolds under pseudosymmetric conditions.
method Examining the pseudosymmetric type condition \( R \cdot R = L_1 Q(g,R) + L_2 Q(S,R) \) and evaluating the characterization theorem.
result Necessary and sufficient conditions for various pseudosymmetric types in warped product manifolds.
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.
The study proves that geodesic spherical curves characterize manifolds of constant curvature.
problem Characterizing manifolds of constant curvature using spherical curves.
method Proving the converse of the known linear equation for RM frames, and providing two additional characterizations.
result Geodesic spherical curves on a manifold characterize constant sectional curvature.
Several characterizations of umbilic points of submanifolds in arbitrary Riemannian and Lorentzian manifolds are given. As a consequence, we obtain new characterizations of spheres in the Euclidean space and of hyperbolic spaces in the Lorentz-Minkowski space. We also prove the Lorentzian version of a classical result …
The study characterizes Sasakian manifolds from magnetic Hopf surfaces.
problem Characterizing Sasakian manifolds from magnetic Hopf surfaces.
method Using a unit Killing vector field and Lie dragging a magnetic curve, the study characterizes Sasakian structures.
result If a magnetic Hopf surface is a constant mean curvature surface, then the manifold M is a Sasakian manifold.