We present short proofs of Toruńczyk's well-known characterization theorems of the Hilbert cube and Hilbert space, respectively.
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48 results for “characterization theorems”
We review several results related to the characterization of polyhedra in hyperbolic 3-space. In particular we present Rivin's theorem that gives a characterization of compact convex hyperbolic polyhedra, and Hodgson's proof of the Adreev's theorem. We also review the analogous characterization of ideal polyhedra, and …
We characterize the convexity of functions and the monotonicity of vector fields on metric measure spaces with Riemannian Ricci curvature bounded from below. Our result offers a new approach to deal with some rigidity theorems such as `splitting theorem' and `volume cone implies metric cone theorem' in non-smooth conte…
The paper geometrically characterizes graded manifolds and proves the Frobenius theorem.
problem Understanding and characterizing graded manifolds.
method Geometric characterization and Frobenius theorem proof.
result Frobenius theorem proven for graded distributions.
In this paper, firstly the axis of a slant helix is found with a method. Secondly, the theorem which characterizes a unit speed curve to be a slant helix is proved in detail. The importance of this theorem is stemed from that it has led to many papers regarding slant helices in the differential geometry literature.
In this paper, we mainly prove a theorem with a corollary establishing two characterizations of the Calabi composition of hyperbolic hyperspheres, where the second characterization (i.e., the corollary) has been given via a dual correspondence theorem earlier but now we would like to use a very direct method. Note that…
New curvature condition helps characterize Kähler manifolds.
problem Characterize compact Kähler manifolds with specific curvature properties.
method Introduce and utilize positive bisectional curvature condition.
result Deduce characterization theorem for manifolds with positive bisectional curvature.
SL(n) covariant valuations on Orlicz spaces are represented and characterized.
problem Representing SL(n) covariant valuations on Orlicz spaces.
method Representation theorem established for continuous, SL(n) covariant vector-valued valuations.
result Unique characterization of SL(n) covariant valuations as moment vectors.
Characterizes density-valued symplectic forms on multisymplectic manifolds.
problem Understanding density-valued symplectic forms on multisymplectic manifolds.
method Intrinsic characterization and Darboux-type theorems.
result Proves Darboux-type theorems for density-valued symplectic forms.
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.
First geometric proof of the flyping theorem.
problem Proving Tait's flyping conjecture.
method Geometric proof using Greene's characterization, Menasco's crossing ball structures, and isotopy/re-plumbing moves.
result First entirely geometric proof of Menasco-Thistlethwaite's flyping theorem.
Characterizes simplicial complexes embedding into spheres with few vertices.
problem Characterizing simplicial complexes that embed into spheres with few vertices.
method Simple characterization using non-face families and analogy with Fáry's theorem.
result Recovery of van Kampen--Flores theorem and Erd\H os--Ko--Rado theorem.
This paper is devoted, first of all, to give a complete unified proof of the Characterization Theorem for compact generalized Kähler manifolds (Theorem 3.2). The proof is based on the classical duality between "closed" positive forms and "exact" positive currents. In the last part of the paper we approach the gener…
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.
We give a combinatorial characterization of generic minimal rigidity for planar periodic frameworks. The characterization is a true analogue of the Maxwell-Laman Theorem from rigidity theory: it is stated in terms of a finite combinatorial object and the conditions are checkable by polynomial time combinatorial algorit…
We consider closed orientable hypersurfaces in a wide class of warped product manifolds, which include space forms, deSitter-Schwarzschild and Reissner-Nordström manifolds. By using a new integral formula or Brendle's Heintze-Karcher type inequality, we present some new characterizations of umbilic hypersurfaces. These…
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 curvature positivity for Riemannian metrics on flat vector bundles.
problem Characterizing Nakano positivity of Riemannian flat vector bundles.
method Using solvability of the equation with specific estimates and inspired by recent works on Hermitian holomorphic vector bundles.
result Alternative proof of matrix-valued Prekopa's theorem.
Let be a principal fiber bundle and be an associate fiber bundle. Our interested is to study harmonic sections of the projection of into . Our first purpose is to give a stochastic characterization of harmonic section from into and a geometric characterization of harmonic se…
The paper proves unique characterization of gravitational instantons with specific volume growth.
problem Characterizing gravitational instantons with quadratic volume growth.
method Defining a period mapping and proving its surjectivity and openness.
result The periods uniquely characterize ALG and ALG gravitational instantons up to diffeomorphism.
Study on lightlike submanifolds in statistical manifold geometry.
problem Characterizing contact CR and SCR-lightlike submanifolds.
method Developed characterization theorems on integrability and geodesicity.
result Obtained results on geometry of contact CR and SCR-lightlike submanifolds.
The two main theorems of this paper provide a characterization of hyperbolic affine iterated function systems defined on Rm. Atsushi Kameyama (Distances on Topological Self-Similar Sets, Proceedings of Symposia in Pure Mathematics, Volume 72.1, 2004) asked the following fundamental question: given a topological self-si…
In this note we present various extensions of Obata's rigidity theorem concerning the Hessian of a function on a Riemannian manifold. They include general rigidity theorems for the generalized Obata equation, and hyperbolic and Euclidean analogs of Obata's theorem. Besides analyzing the full rigidity case we also chara…
The paper characterizes curvature-dimension conditions and related inequalities on Riemannian manifolds.
problem Curvature-dimension conditions and related inequalities on Riemannian manifolds.
method Information-theoretic approach to study curvature-dimension condition, rigidity theorems, and entropy differential inequalities.
result Equivalence of curvature-dimension condition and entropy differential inequalities on Riemannian manifolds.
Study provides concrete examples of knot slopes.
problem Finding explicit characterizing slopes for knots.
method Concrete examples for the (-2,3,7)-pretzel knot.
result Explicit characterizing slopes for the knot .
In this paper, we prove a similar result to the fundamental theorem of regular surfaces in classical differential geometry, which extends the classical theorem to the entire class of singular surfaces in Euclidean 3-space known as frontals. Also, we characterize in a simple way these singular surfaces and its fundament…
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 -plurisubharmonic functions, established GH embeddings.
result Characterized GC Stein manifolds via -plurisubharmonic exhaustion functions and GH embeddings.
Characterizes adequate links using Jones polynomial and crossing number.
problem Characterizing adequate links.
method Using Jones polynomial and crossing number, proving links are adequate.
result Links with specific polynomial properties are adequate.
Unified proof of Nielsen-Thurston classification via Teichmüller's theorem.
problem Classifying mapping class groups and rational maps.
method Unified proof following Bers' approach.
result Unified proof of Nielsen-Thurston classification.
The unit ball is characterized by a Kähler-Einstein potential.
problem Characterizing the unit ball in complex geometry.
method Using a global potential function of the Kähler-Einstein metric.
result A compact Kähler manifold with an ample canonical bundle is the unit ball if it has a specific potential function.
In this paper, we first establish an equivalence theorem of Minkowski spaces by using results in centro-affine differential geometry. As an application in Finsler geometry, we gives some new characterizations of Berwald spaces.
The study characterizes and verifies equivariant embeddings of symmetric Kählerian manifolds.
problem Characterizing and verifying equivariant embeddings of symmetric Kählerian manifolds.
method Investigation motivated by Cartan and Wallach's theorem on symmetric spaces, focusing on and parallel plurimean curvature.
result If an equivariant embedding has parallel plurimean curvature, it is the extrinsically symmetric one.
Stokes' theorem's boundary maximizes entropy.
problem Characterizing the boundary of a manifold using entropy.
method Maximizing entropy for codimension-1 submanifolds satisfying Stokes' theorem.
result The boundary of a manifold maximizes the entropy functional.
We refine Theorem A due to Gursky \cite{G3}. As applications, we give some rigidity theorems on four-manifolds with postive Yamabe constant. In particular, these rigidity theorems are sharp for our conditions have the additional properties of being sharp. By this we mean that we can precisely characterize the case of e…
The study characterizes hypersurfaces in spheres with constant scalar curvature.
problem Characterizing hypersurfaces in spheres with constant scalar curvature.
method Combining intrinsic and extrinsic geometry, establishing Takahashi-type theorems, and deriving integral inequalities.
result Characterizes hypersurfaces with specific curvature properties and provides spherical Bernstein theorems.
Extends Polydisk Theorem to Cartan-Hartogs domains.
problem Characterizing geodesics in Cartan-Hartogs domains.
method Applying the Polydisk Theorem to Cartan-Hartogs domains.
result Cartan-Hartogs domains inherit geodesic submanifolds from bounded symmetric domains.
Haefliger cohomology characterizes taut foliated manifolds by Haefliger's theorem. We show that Haefliger cohomology characterizes strongly tense foliated manifolds, namely, foliated manifolds which admit a Riemannian metric such that the mean curvature form of the leaves is closed and basic. We show that Haefliger coh…
We establish Marstrand-type projection theorems for orthogonal projections along geodesics onto m-dimensional subspaces of hyperbolic -space by a geometric argument. Moreover, we obtain a Besicovitch-Federer type characterization of purely unrectifiable sets in terms of these hyperbolic orthogonal projections.
Multi-Time KCC-Invariantsmath.DG
In this paper we construct some multi-time geometrical extensions of the KCC-invariants, which characterize a given second-order system of PDEs on the 1-jet space . A theorem of characterization of these multi-time geometrical KCC-invariants is given.
In this paper we provide a sharp characterization of the smooth four-dimensional sphere. The assumptions of the theorem are conformally invariant, and can be reduced to an L^2 inequality of the Weyl tensor and positivity of the Yamabe invariant.
The paper applies Clairaut's theorem to rotational surfaces in pseudo-Euclidean 4-space.
problem Exploring geodesic curves on rotational surfaces in pseudo-Euclidean 4-space.
method Expressing Clairaut's theorem and deriving equations for geodesic curves.
result Characterization of geodesic curves on hyperbolic and elliptic surfaces of rotation.
Paper generalizes Andreev's theorem with obtuse angles.
problem Characterizing hyperbolic polyhedra with obtuse angles.
method Established discrete analog of weak solution/regularity theory.
result Generalized Andreev's Theorem to include obtuse angles.
A new characterization of the CR shpere and the sharp eigenvalue estimate for the Kohn Laplacianmath.DG
Motivated by a sharp eigenvalue estimate for the Kohn Laplacian, we prove a theorem that characterizes the CR sphere in terms of the existence of a non-trivial complex-valued function satisfying a certain overdetermined system.
This paper is concerned with "nice" compactifications of manifolds. Siebenmann's iconic dissertation characterized open manifolds M^m (m>5) compactifiable by addition of a manifold boundary. His theorem extends easily to cases where M^m is noncompact with compact boundary; however, when Bd(M^m) is noncompact, the situa…
In this paper we construct the jet geometrical extensions of the KCC-invariants, which characterize a given second-order system of differential equations on the 1-jet space . A generalized theorem of characterization of our jet geometrical KCC-invariants is also presented.
We extend Forester's rigidity theorem so as to give a complete characterization of rigid group actions on trees (an action is rigid if it is the only reduced action in its deformation space, in particular it is invariant under automorphisms preserving the set of elliptic subgroups).
This is the second of two papers that describe a compactness theorem for sequences of solutions of certain SL(2;C) analogs of the anti-self dual equations on oriented, 4-dimensional Riemannian manifolds. This paper proves theorems that characterize the singular locus of limits of sequences of solutions to the equations…
We generalize Hagopian's theorem characterizing solenoids to higher dimensions by showing that any homogeneous continuum admitting a fiber bundle projection onto a torus with totally disconnected fibers admits a compatible abelian topological group structure. The higher dimensional exponent group is then introduced.