Recently, it is proven that generalized Robertson-Walker space-times in all orthogonal subspaces of Gray's decomposition but one(unrestricted) are perfect fluid space-times. GRW space-times in the unrestricted subspace are identified by having constant scalar curvature. Generalized quasi-Einstein GRW space-times have a…
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48 results for “general spaces”
Smooth distributions on subcartesian spaces can be globally finitely generated.
problem Understanding smooth distributions on subcartesian spaces.
method Embedding in Euclidean space, Whitney Embedding Theorem, and distribution theory.
result Smooth generalized distributions and subbundles on connected subcartesian spaces are globally finitely generated.
New examples of structures found using twistor space.
problem Finding non-trivial generalized paracomplex structures.
method Twistor space construction scheme.
result Non-trivial examples of generalized paracomplex structures constructed.
Paper studies second order symmetric parallel tensors in generalized f.pk-space forms.
problem Exploring properties of second order symmetric parallel tensors in generalized f.pk-space forms.
method Analyzes the properties of second order symmetric parallel tensors and deduces the existence or non-existence of certain tensors and hypersurfaces.
result There does not exist second order skew-symmetric parallel tensor in f.pk-space form. There is no parallel hypersurface in a generalized f.pk-space form but there is semi-parallel hypersurface.
General Casorati inequalities and implications for Riemannian maps and Riemannian submersionsmath.DG
The paper establishes new Casorati inequalities for various Riemannian maps and submersions.
problem Developing new inequalities for Riemannian maps and submersions.
method Using general forms of Casorati inequalities, the paper derives inequalities for specific Riemannian spaces.
result The paper provides new Casorati inequalities for Riemannian maps and submersions.
Classifies generalized Seifert fiber spaces and their branched covers.
problem Classifying generalized Seifert fiber spaces and their topological properties.
method Symbolic classification and computation of invariants.
result Canonical double branched cover of non-manifold spaces is a Seifert manifold.
GLAD improves latent graph generation by quantizing discrete latent space.
problem Latent space graph generative models lack performance and make unnatural assumptions.
method Adapting diffusion bridges to a discrete latent space, avoiding data space decompositions.
result GLAD achieves competitive performance on graph benchmark datasets.
We classify generalized Wallach spaces which are g.o. spaces. We also investigate homogeneous geodesics in generalized Wallach spaces for any given invariant Riemannian metric and we give some examples.
The twistor construction for Riemannian manifolds is extended to the case of manifolds endowed with generalized metrics (in the sense of generalized geometry à la Hitchin). The generalized twistor space associated to such a manifold is defined as the bundle of generalized complex structures on the tangent spaces of the…
We consider biharmonic submanifolds in both generalized complex and Sasakian space forms. After giving the biharmonicity conditions for submanifolds in these spaces, we study different particular cases for which we obtain curvature estimates. We consider curves, complex and Lagrangian surfaces and hypersurfaces for the…
Local reflexion spacesmath.DG
A reflexion space is generalization of a symmetric space introduced by O. Loos. We generalize locally symmetric spaces to local reflexion spaces in the similar way. We investigate, when local reflexion spaces are equivalently given by a locally flat Cartan connection of certain type.
Generalized Laurent monomials for nonrational spaces.
problem Handling singular spaces in toric geometry.
method Extending Laurent monomials to nonrational toric quasifolds.
result Generalized Laurent monomials defined for nonrational toric quasifolds.
Generative models use Riemannian manifolds to improve latent space interpretation.
problem Generative models often bias latent space interpretations.
method Use Riemannian manifolds to define latent space paths that respect ambient geometry.
result Improves interpretability of learned representations for both stochastic and deterministic generators.
Generatability in metric spaces studied with novel novelty parameters.
problem Understanding generatability in metric spaces with asymmetric novelty parameters.
method Introducing -closure dimension to characterize uniform and non-uniform generatability.
result Generatability is stable across novelty scales in doubling spaces but can be highly scale-sensitive in general metric spaces.
Study explores weak generalized K-contact structures in contact metric spaces.
problem Exploring weak generalized K-contact structures in contact metric spaces.
method Introducing a weak condition and proving existence of K-contact and -structures.
result Existence of K-contact and -structures under certain conditions on the Boeckx invariant.
This paper generalizes optimization techniques to diffeological spaces.
problem Challenges in applying optimization techniques to diffeological spaces due to various tangent space definitions.
method Suitable definition of tangent space, diffeological Riemannian space, diffeological gradient, and diffeological retraction.
result Formulation of an optimization algorithm on diffeological spaces.
Bielavsky introduced and investigated the class of symmetric symplectic spaces, that is, symmetric spaces endowed with a symplectic form invariant with respect to symmetries. Since the theory of symmetric spaces has generalizations, we ask a question about their possible symplectic versions. We do construct such genera…
Paper establishes new inequality for Riemannian maps and applies it to various space forms.
problem Developing a new inequality for Riemannian maps and its applications.
method Proposed and utilized a general Chen's first inequality for Riemannian maps and applied it to various space forms.
result Validated the new inequality and compared results with existing approaches.
A minimal space-like surface in Minkowski space-time is said to be of general type if it is free of degenerate points. The fact that minimal space-like surfaces of general type in Minkowski space-time admit canonical parameters of the first (second) type implies that any minimal space-like surface is determined uniquel…
Diffeological spaces are generalizations of smooth manifolds which include singular spaces and function spaces. For each diffeological space, Iglesias-Zemmour introduced a natural topology called the -topology. However, the -topology has not yet been studied seriously in the existing literature. In this paper, we…
We introduce the notion of Hamiltonian spaces for Manin pairs over manifolds, using the so-called generalized Dirac structures. As an example, we describe Hamiltonian spaces of a quasi-Lie bialgebroid using this general framework. We also discuss reduction of Hamiltonian spaces of this general type.
Proves Mayer-Vietoris sequence for diffeological spaces using generating families.
problem No specific problem stated; focuses on extending a sequence.
method Uses generating families instead of coverings in diffeological spaces.
result Proves a Mayer-Vietoris sequence for diffeological spaces.
Unified framework for Alexandrov 3-spaces, extending manifold results.
problem Extend manifold topology results to Alexandrov 3-spaces.
method Generalize connected sum, prime decomposition, and Dehn surgery.
result Unified framework for Alexandrov 3-spaces, including non-manifold spaces.
Metrizability of the Lie algebroid generalized tangent bundle and (generalized) Lagrange -spacesmath.DG
A class of metrizable vector bundles in the general framework of generalized Lie algebroids have been presented in the eight reference. Using a generalized Lie algebroid we obtain the Lie algebroid generalized tangent bundle of a vector bundle. This Lie algebroid is a new example of metrizable vector bundle. A new clas…
We describe moduli spaces of invariant generalized complex structures and moduli spaces of invariant generalized Kähler structures on maximal flag manifolds under -transformations. We give an alternative description of the moduli space of generalized complex structures using pure spinors, and describe a cell decompo…
The distance function (or ) of a distance space (general metric space) is not differentiable in general. We investigate such distance spaces over , whose distance functions are differentiable like in case of Finsler spaces. These spaces have several good properties, yet they are no F…
Hidden symmetries and the generic spectral setting of generalized laplacians on homogeneous spacesmath.DG
Study spectral settings of generalized Laplacians on homogeneous spaces.
problem Understanding the spectral properties of generalized Laplacians on compact homogeneous spaces.
method Investigates the generic spectral configuration of operators on -invariant metrics on .
result The spectral setting depends on -isometries and hidden symmetries.
The Cantor Riemanniummath.CV
Cantor Riemannium is a new type of space from holomorphic germs.
problem Defining a new type of space from holomorphic germs.
method Constructing the Cantor Riemannium by Borel monogenic continuation.
result The Cantor Riemannium is a metric, path connected, Gromov length space.
The paper examines conditions for conformal Ricci solitons on generalized ()-space forms.
problem Conditions for conformal Ricci solitons on generalized ()-space forms.
method Derivation of conditions for solitons to be shrinking, steady, or expanding in terms of conformal pressure p.
result Conditions for a Ricci semi-symmetric generalized ()-space form to form an Einstein manifold when equipped with a conformal Ricci soliton.
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.
Study shows quotient group is infinitely generated.
problem Understanding the structure of homology cobordism groups.
method Proved using Seifert fibered spaces.
result Quotient group is infinitely generated.
Proposes CLSM for better subsequence generation in music sequences.
problem Editing subsequences in music sequences without losing context.
method Context-informed prior and decoder for generative model, context position-informed encoder for inference.
result Contextual latent space is smoother in interpolation and generates higher quality samples.
Centrally Harmonic spacesmath.DG
Constructs examples of centrally harmonic spaces and shows they are not generically harmonic.
problem Understanding conditions for centrally harmonic spaces.
method Generalizing work of Copson and Ruse to construct examples.
result Examples of centrally harmonic spaces are not generically harmonic.
New infinite families of flat spaces found from symmetric spaces.
problem Finding new flat homogeneous spaces.
method Starting from compact symmetric spaces, constructing infinite families of compact homogeneous spaces with invariant Bismut connections.
result Infinite families of compact homogeneous spaces with vanishing Ricci tensor.
It is shown that four-dimensional generalized symmetric spaces can be naturally equipped with some additional structures defined by means of their curvature operators. As an application, those structures are used to characterize generalized symmetric spaces.
A Wasserstein spaces is a metric space of sufficiently concentrated probability measures over a general metric space. The main goal of this paper is to estimate the largeness of Wasserstein spaces, in a sense to be precised. In a first part, we generalize the Hausdorff dimension by defining a family of bi-Lipschitz inv…
Basic Classes of Timelike General Rotational Surfaces in the Four-dimensional Minkowski Spacemath.DG
Study of timelike surfaces in Minkowski space with specific geometric properties.
problem Characterizing geometric properties of timelike surfaces in Minkowski space.
method Analytical study of two types of timelike general rotational surfaces.
result Explicit descriptions of minimal and surfaces with specific curvature properties.
Word metrics from large balls in injective spaces are exponentially generic and growth tight.
problem Understanding genericity and growth in word metrics from injective spaces.
method Geometric arguments and large ball considerations.
result Exponential genericity and growth tightness for word metrics.
State-space systems generate probabilistic dependencies between inputs and outputs.
problem Understanding probabilistic dependencies in state-space systems.
method Introducing a probabilistic framework and proving sufficient conditions for output existence and uniqueness.
result State-space systems can generate probabilistic dependencies, even without functional relations.
This note finds explicit representatives for moduli space of parabolic bundles.
problem Finding explicit representatives in deRham cohomology for the moduli space of parabolic bundles.
method Using results from vector bundles and computing intersection pairing of cohomology.
result Explicit representatives in deRham cohomology for the generators of the moduli space of parabolic bundles.
Study on cones over metric spaces with curvature bounds.
problem Establishing curvature bounds for cones over metric spaces.
method Developed a localization technique to prove synthetic curvature bounds.
result Riemannian and Lorentzian cones over CD-spaces satisfy MCP and vice versa.
Defines a new Poisson structure for generalized Sasakian spaces.
problem No specific problem stated; focuses on new structure definition.
method Defines a canonical Poisson structure on generalized contact metric spaces.
result Shows distinction between generalized Sasakian and coKähler structures.
Generative models for function-valued data in infinite dimensions.
problem Lack of semantics relating discretized data to underlying functional forms.
method Generalized diffusion models to function space, using Gaussian measures on Hilbert spaces.
result Explicit specification of function space allows unconditional and conditional generation of function-valued data.
New quasimetric spaces improve stability in complex Hessian equations.
problem Improving stability results for complex Hessian equations.
method Constructing a family of quasimetric spaces in generalized potential theory.
result Convergence of quasimetric spaces leads to improved stability results.
In this paper we address what generalized geometric structures are possible on products of spaces that each admit generalized geometries. In particular we consider, first, the product of two odd dimensional spaces that each admit a generalized almost contact structure, and then subsequently, the product of an odd dimen…
Generalizations of the Weierstrass formulae to generic surface immersed into , and into multidimensional Riemann spaces are proposed. Integrable deformations of surfaces in these spaces via the modified Veselov-Novikov equation are discussed.
Killing tensors on complex projective space are identified and generated by Killing fields.
problem Identifying Killing tensors on complex projective space.
method Determining Killing tensors of arbitrary rank on complex projective space with Fubini-Study metric.
result Complex projective spaces are generated by Killing fields.
We describe the moduli space of extensions in the model category of simplicial presheaves. This article can be seen as a generalization of Blomgren-Chacholski results in the case of simplicial sets. Our description of the moduli space of extensions treat the equivariant and the nonequivariant case in the same setting. …