The paper studies special warped products with a specific connection on super Riemannian manifolds.
problem Investigating curvature and Ricci tensors on super warped product spaces with a semi-symmetric non-metric connection.
method Defined a semi-symmetric non-metric connection, computed curvature and Ricci tensors, and introduced and analyzed two types of super warped product spaces.
result Conditions for two super warped product spaces with a semi-symmetric non-metric connection to be Einstein spaces are provided.
The paper studies a new connection on Riemannian manifolds and finds conditions for symplectic manifolds.
problem Exploring a new quarter-symmetric non-metric connection on Riemannian manifolds.
method Analyzes the properties and relations of the torsion tensor and curvature tensors of the new connection.
result Conditions for a manifold to be symplectic when endowed with the new connection.
The object of this paper is to obtain the concircular curvature tensor of the semi symmetric non-metric connection on the Weyl manifold and to give a necessary and sufficient condition for a semi symmetric non-metric connection to be S-concircular.
We present a homogenization theorem for isotropically-distributed point defects, by considering a sequence of manifolds with increasingly dense point defects. The loci of the defects are chosen randomly according to a weighted Poisson point process, making it a continuous version of the first passage percolation model.…
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…
The paper extends gradient flow and relaxation studies to non-flat Riemannian manifolds.
problem Understanding gradient flows and relaxation in non-flat Riemannian manifolds.
method Developed a criterion for comparing relaxation along gradient descent curves using non-metricity tensor.
result Revealed a universal asymmetry: warming up is faster than cooling down.
Necessary and sufficient conditions for some deformation algebras to provide formal Frobenius structures are given. Also, examples of formal Frobenius structures with fundamental tensor that is not of the deformation type and examples of symmetric non-metric connections are presented.
The study investigates properties of a specific Riemannian manifold with a semi-symmetric non-metric connection.
problem Characterizing properties of a Riemannian manifold with a semi-symmetric non-metric connection.
method Construction of a non-trivial example, proving manifold properties based on the metric being a gradient soliton or Yamabe soliton.
result A manifold with a semi-symmetric non-metric connection and gradient Ricci/Yamabe soliton is of constant curvature.
H. A. Hayden [1] introduced the idea of semi-symmetric non-metric connection on a Riemannian manifold in (1932). Agashe and Chafle \cite{1} defined and studied semi-symmetric non-metric connection on a Riemannian manifold. In the present paper, we define a new type of semi-symmetric non-metric connexion in an almost co…
New proof shows Cohen-Lyndon property for non-metric small-cancellation.
problem Proving the Cohen-Lyndon property in non-metric settings.
method Generalized metric small-cancellation results.
result Cohen-Lyndon property holds for non-metric small-cancellation quotients.
The aim of the present paper is to study the properties of Kenmotsu manifolds equipped with a non-symmetric non-metric connection. We also establish some curvature properties of Kenmotsu manifolds. It is proved that a Kenmotsu manifold endowed with a non-symmetric non-metric is irregular.
In this paper, we study the Einstein multiply warped products with a semi-symmetric non-metric connection and the multiply warped products with a semi-symmetric non-metric connection with constant scalar curvature, we apply our results to generalized Robertson-Walker spacetimes with a semi-symmetric non-metric connecti…
Paper derives inequalities for submanifolds in a specific geometric space.
problem Chen's inequalities for submanifolds in (κ,μ)-contact space form. method Using generalized semi-symmetric non-metric connections.
result Derives new inequalities for submanifolds.
Paper establishes inequality for submanifolds in real space forms with semi-symmetric non-metric connection.
problem Deriving a sharp lower bound for Ricci curvature of submanifolds.
method Using semi-symmetric non-metric connection, derive a lower bound for Ricci curvature in terms of mean curvature vector and second fundamental form.
result Established Hineva inequality for submanifolds with semi-symmetric non-metric connection.
The paper studies geometric structures of wormholes using a new connection.
problem Exploring new geometric properties of wormholes.
method Extended Levi-Civita connection to semi-symmetric non-metric connections.
result Morris-Thorne wormholes exhibit specific geometric properties.
The aim of this paper is to study generalized recurrent, generalized Ricci-recurrent, weakly symmetric and weakly Ricci-symmetric Kenmotsu manifolds with respect to the semi-symmetric non-metric connection.
We show that both, the Jordan curve theorem and the Schoenflies theorem extend to non-metric manifolds (at least in the two-dimensional context), and conclude by some dynamical applications à la Poincaré-Bendixson.
Study characterizes submanifolds in metallic semi-Riemannian manifolds with specific connections.
problem Characterizing submanifolds in metallic semi-Riemannian manifolds.
method Introduces and analyzes invariant and screen semi-invariant lightlike submanifolds with a quarter symmetric non-metric connection.
result Characterizes integrability and parallelism of distributions in these submanifolds.
The paper studies geometric structures in Sol_3 with two connections.
problem Analyzing geometric structures in Sol_3 using specific connections.
method Used Levi-Civita and semi-symmetric non-metric connections to study Sol_3.
result Concluded geometric structures in Sol_3 with both connections.
New formulation of Schrödinger connections preserves vector lengths in geometry.
problem Preserving vector lengths in non-Euclidean geometries.
method Coordinate-free formulation, differential geometry, torsion, non-metricity.
result Explicit example of non-static Einstein manifold with torsion.
In this paper, we study non integrable distributions in a Riemannian manifold with a semi-symmetric metric connection, a semi-symmetric non-metric connection and a statistical connection. We obtain the Gauss, Codazzi, and Ricci equations for non integrable distributions with respect to the semi-symmetric metric connect…
Study on surfaces with constant curvature under a specific connection.
problem Classifying surfaces with constant sectional curvature under a semi-symmetric non-metric connection.
method Analyzing surfaces in R3 with a canonical semi-symmetric non-metric connection determined by a vector field. result Classification of surfaces under various conditions (cylindrical, rotational) with constant sectional curvature.
In this paper we continue the study of bi-conformal vector fields started in {\em Class. Quantum Grav.} {\bf 21} 2153-2177. These are vector fields defined on a pseudo-Riemannian manifold by the differential conditions $\lie P_{ab}=φP_{ab}$, $\lieΠ_{ab}=χΠ_{ab}$ where Pab, Πab are orthogonal and complementary…
Topolow embeds dissimilarity data into Euclidean space robustly against non-metricity and sparsity.
problem Embedding dissimilarity data into Euclidean space when dissimilarities are non-metric or sparse.
method Topolow uses a physics-inspired, gradient-free optimization framework to maximize likelihood under a Laplace error model.
result Topolow outperforms standard MDS methods in reconstructing sparse and non-Euclidean data.
Develops torsion dual connections for statistical manifolds.
problem Defining statistical manifolds using dual connections.
method Introduces torsion dual connections and proves their properties.
result Curvature tensor of torsion dual connections has specific divergence.
Develops method to compute Chern-Simons potentials from higher-dimensional Pontryagin densities.
problem Computing Chern-Simons potentials from higher-dimensional Pontryagin densities.
method Systematic approach using a generic affine connection with non-vanishing torsion and non-metricity.
result Algorithm and code for determining Chern-Simons potential from Pontryagin density in arbitrary even dimensions.
A little complement concerning the dynamics of non-metric manifolds is provided, by showing that any flow on an ω-bounded surface with non-zero Euler character has a fixed point.
We show that a large class of non-metric, non-symplectic affine holonomies can be realized, uniformly and without case by case considerations, by Weyl connections associated to the natural AHS-structures on certain generalized flag manifolds.
The paper studies affine connections on singular warped products and their curvature.
problem Analyzing affine connections on singular warped products.
method Introducing semi-symmetric metric and non-metric Koszul forms, and expressing their curvature in terms of factor manifolds.
result Generalized results for singular multiply warped products.
The present paper deals with some results of submanifolds of generalized Sasakian-space-forms in \cite{ALEGRE3} with respect to semisymmetric metric connection, semisymmetric non-metric connection, Schouten-van Kampen connection and Tanaka-webster connection.
The paper classifies geometric structures of δ-almost Yamabe solitons on paracontact metric manifolds.
problem Characterizing δ-almost Yamabe solitons on paracontact metric manifolds.
method Investigation of geometric structures under specific assumptions, including quarter-symmetric non-metric connections.
result Conditions for δ-almost Yamabe solitons to be expanding, steady, or shrinking.
Complex embeddings handle non-metric proximity data better than traditional methods.
problem Proximities not always metric or inner product-based, causing convergence issues.
method Proposes complex-valued embeddings for non-vectorial data.
result Complex embeddings outperform traditional techniques on benchmarks.
The present paper deals with some results of almsot semi-invariant submanifolds of generalized Sasakian-space-forms in \cite{ALEGRE3} with respect to semisymmetric metric connection, semisymmetric non-metric connection, Schouten-van Kampen connection and Tanaka-Webster connection.
New insights into metrizability of SO(3)-invariant connections, linking Riemann and Finsler structures.
problem Clarifying metrizability of SO(3)-invariant connections between Riemann and Finsler structures.
method Analyzing 4D SO(3)-invariant, Berwald-Finsler metrizable connections to find non-metric but metrizable connections.
result Identified classes of SO(3)-invariant connections that are not Levi-Civita connections for any pseudo-Riemannian metric but can still be metrized by Finsler functions.
Study of minimal surfaces in 3D space with special connections.
problem Classification of minimal translation surfaces in Euclidean spaces with semi-symmetric connections.
method Analysis of singular minimal translation surfaces in a 3D Euclidean space with a semi-symmetric connection.
result Classification of singular minimal translation surfaces in Euclidean spaces with semi-symmetric connections.
We investigate L-sectional curvature of S-manifolds with respect to the Rieman- nian connection and to certain semi-symmetric metric and non-metric connections naturally related with the structure, obtaining conditions for them to be constant and giving examples of S-manifolds in such conditions. Moreover, we calculate…
Classical elasticity is concerned with bodies that can be modeled as smooth manifolds endowed with a reference metric that represents local equilibrium distances between neighboring material elements. The elastic energy associated with a configuration of a body in classical elasticity is the sum of local contributions …
In a general and non metrical framework, we introduce the class of CR quaternionic manifolds containing the class of quaternionic manifolds, whilst in dimension three it particularizes to, essentially, give the conformal manifolds. We show that these manifolds have a rich natural Twistor Theory and, along the way, we o…
The Optimal transport (OT) problem is rapidly finding its way into machine learning. Favoring its use are its metric properties. Many problems admit solutions with guarantees only for objects embedded in metric spaces, and the use of non-metrics can complicate solving them. Multi-marginal OT (MMOT) generalizes OT to si…
In a general and non metrical framework, we introduce the class of co-CR quaternionic manifolds, which contains the class of quaternionic manifolds, whilst in dimension three it particularizes to give the Einstein-Weyl spaces. We show that these manifolds have a rich natural Twistor Theory and, along the way, we obtain…
Unified framework for hyperbolic embeddings from mixed data types.
problem Computing hyperbolic embeddings from noisy metric and non-metric data.
method Semidefinite programming and spectral factorization methods.
result Efficient computation of hyperbolic embeddings from arbitrary data.
The study classifies minimal translation surfaces in 3D and 3D_1.
problem Classifying minimal translation surfaces in specific geometric settings.
method Defined and classified minimal translation surfaces with semi-symmetric connections.
result New classification of minimal translation surfaces in R3 and R13. Theory of Newtonian dynamical systems admitting normal shift of hypersurfaces was first developed for the case of Riemannian manifolds. Recently it was generalized for manifolds geometric equipment of which is given by some regular Lagrangian or, equivalently, by some regular Hamiltonian dynamical system. In present pa…
Detect spacetime curvature without rulers and clocks in 3D.
problem Detecting spacetime curvature without traditional measurement tools.
method Generalized results from 2D to 3D spacetime, proving well-stitched spacetime for conformally flat cases.
result A 3D spacetime is well-stitched if and only if it is conformally flat, providing a tool for curvature detection.
We prove optimal bounds for the convergence rate of ordinal embedding (also known as non-metric multidimensional scaling) in the 1-dimensional case. The examples witnessing optimality of our bounds arise from a result in additive number theory on sets of integers with no three-term arithmetic progressions. We also carr…
We construct several examples of compactifications of Einstein metrics. We show that the Eguchi--Hanson instanton admits a projective compactification which is non--metric, and that a metric cone over any (pseudo)--Riemannian manifolds admits a metric projective compactification. We construct a para--c--projective co…
We introduce higher order mean curvatures of screen almost conformal (SAC) half-lightlike submanifolds of indefinite contact manifolds, admitting a semi-symmetric non-metric connection, and use them to generalize some known results of [6]. Also, we derive a new set of integration formulae via the divergence of some spe…
Proposes FMC for fair clustering with independent parameters.
problem Finding clusters with balanced sensitive attribute proportions.
method Model-based clustering using finite mixture model with mini-batch learning.
result FMC scales up easily and can handle non-metric data.