Study examines properties of a specific type of geometric immersion.
problem Understanding geometric properties of doubly twisted product immersions.
method Established basic geometric properties through analysis.
result Basic geometric properties of doubly twisted product immersions have been identified.
Characterizes a specific type of spacetime using vector fields.
problem Classifying a specific type of spacetime.
method Using vector fields to characterize 1+n doubly twisted spacetimes.
result Simple classification of 1+n doubly-twisted spacetimes.
Characterizes spacetimes using doubly torqued vectors.
problem Classifying spacetimes based on their geometric properties.
method Characterization through doubly torqued vectors and their properties.
result Doubly twisted and Kundt spacetimes can be characterized.
The twisting number of a ribbon knot is at least as large as its doubly slice genus.
problem Proving a lower bound for the twisting number of ribbon knots in terms of their doubly slice genus.
method Analyzing symmetric unions and tangle replacements to establish the bound.
result Ribbon knots have arbitrarily high twisting numbers, matching their doubly slice genus.
The paper examines Einstein doubly warped product manifolds with a semi-symmetric metric connection.
problem Characterizing Einstein doubly warped product manifolds with a semi-symmetric metric connection.
method Deriving curvature formulas and proving necessary and sufficient conditions for a manifold to be a warped product.
result Obtained results for Einstein doubly warped product manifolds and Einstein-like doubly warped product 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.
Study of conformal vector fields on specific manifolds and their applications.
problem Understanding conformal vector fields on doubly warped product manifolds.
method Complete study of two classes of conformal vector fields and Ricci solitons.
result Characterization of conformal vector fields and their properties.
In this paper we study fundamental geometric properties of doubly warped product immersion which is an extension of warped product immersion. Moreover, we study geometric inequality for doubly warped products isometrically immersed in arbitrary Riemannian manifolds.
We extend classification of doubly slice knots up to 12 crossings.
problem Classifying doubly slice knots with low crossing numbers.
method Alexander module, signature functions, and twisted Alexander polynomials for higher-order branched covers.
result Resolved all but four cases among 2,977 prime knots up to 12 crossings.
Proves conditions for odd pretzel knots to be doubly slice.
problem Identifying conditions for odd pretzel knots to be doubly slice.
method Analyzes knots with specific twist parameters and odd integers.
result Identifies all doubly slice odd pretzel knots.
In this paper, we introduce horizontal and vertical warped product Finsler manifold. We prove that every C-reducible or proper Berwaldian doubly warped product Finsler manifold is Riemannian. Then, we find the relation between Riemmanian curvatures of doubly warped product Finsler manifold and its components, and consi…
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.
In this paper we establish a general inequality involving the Laplacian of the warping functions and the squared mean curvature of any doubly warped product isometrically immersed in a Riemannian manifold. Moreover, we obtain some geometric inequalities for C-totally real doubly warped product submanifolds of generaliz…
The paper examines conditions for Einstein-like classes in doubly warped product manifolds.
problem Conditions for a factor manifold to be in the same Einstein-like class as the entire doubly warped product manifold.
method Analysis of the Ricci tensor and warping functions.
result Sufficient and necessary conditions for a factor manifold to inherit the Einstein-like class of the entire manifold.
The study introduces a new curvature concept for weighted graphs and applies it to warped products.
problem Establishing curvature bounds for doubly warped product graphs.
method Developed a new notion of curvature for weighted graphs and applied it to warped products, establishing bounds in terms of constituent graph curvatures.
result Established curvature bounds for $\left(R_1,R_2
ight)$-doubly warped products of smooth measure spaces.
The paper confirms a conjecture about manifolds with positive curvature.
problem Estimating the width of manifolds with positive sectional curvature.
method Establishing an optimal Lipschitz lower bound for functions on manifolds.
result Characterization of doubly warped product metrics with positive constant curvature.
In this paper biharmonic maps between doubly warped product manifolds are studied. We show that the inclusion maps of Riemannian manifolds B and F into the doubly warped product fB×bF can not be proper biharmonic maps. Also we analyze the conditions for the biharmonicity of projections $_{f}B\times_{b}…
We investigate manifolds obtained as a quotient of a doubly warped product. We show that they are always covered by the product of two suitable leaves. This allows us to prove, under regularity hypothesis, that these manifolds are a doubly warped product up to a zero measure subset formed by an union of leaves. We also…
The paper examines gradient ρ-Einstein solitons on specific manifolds and spacetimes.
problem Characterizing gradient ρ-Einstein solitons on doubly warped product manifolds.
method Analyzing necessary and sufficient conditions for doubly warped product manifolds to be gradient ρ-Einstein solitons, applying results to specific spacetime models.
result No 3-dimensional essentially conformally symmetric gradient ρ-Einstein soliton exists.
Study trisections of spun 4-manifolds from 3-manifolds.
problem Understanding trisections of 4-manifolds from 3-manifolds.
method Local modifications to Heegaard diagrams to create trisection diagrams.
result New 4-manifolds with trisection genus three identified.
In a classic paper Zeeman introduced the k-twist spin of a knot K and showed that the exterior of a twist spin fibers over S^1. In particular this result shows that the knot K # -K is doubly slice. In this paper we give a quick proof of Zeeman's result. The k-twist spin of K also gives rise to two metabolizers for K # …
Warped product CR-submanifolds in Kaehlerian manifolds were intensively studied only since 2001 after the impulse given by B.Y. Chen. Immediately after, another line of research, similar to that concerning Sasakian geometry as the odd dimensional version of Kaehlerian geometry, was developed, namely warped product cont…
Researchers solved a geometry paradox for creased tubes.
problem Resolving the paradox of Gaussian curvature in creased tubes.
method Calculated Gaussian curvature in terms of rate of change of solid angle, dependent on fold angle and curvature.
result Gaussian curvature is zero overall despite the surface being doubly-curved.
Proves volume conjecture for double twist knots using complexified tetrahedrons.
problem Volume conjecture for double twist knots
method Complexified tetrahedron and associated SL(2, C) representation of fundamental group
result Volume conjecture proved for double twist knots
The paper defines and analyzes curvature tensors on super twisted product spaces.
problem Investigating curvature tensors on super twisted product spaces.
method Defined W2-curvature tensor, computed curvature tensors and Ricci tensors, and studied curvature flatness. result Mixed Ricci-flat super twisted product semi-Riemannian manifolds can be expressed as super warped product manifolds.
The paper extends affine connection results to singular warped and twisted products.
problem Generalizing affine connections to singular warped and twisted products.
method Study of singular multiply warped products and singular twisted products with semi-symmetric metric and non-metric connections, discussing Koszul forms and curvature.
result Theoretical results on curvature and Koszul forms for singular multiply warped and twisted products.
Ricci flow on warped products leads to curvature blow-up.
problem Behavior of Ricci flow on warped product metrics.
method Rigorous construction of conical singularities.
result Curvature blows up at a rate proportional to (T−t)−k. In this article we define the twisted product of groups as the generalization of the semidirect product of groups. We will find the necessary and sufficient condition in order that the twisted product of groups to be a group. In particular, for two copies of the same group, the twisted product of group by itself throug…
In this paper, we consider doubly warped product (DWP) Finsler manifolds with some non-Riemannian curvature properties. First, we study Berwald and isotropic mean Berwald DWP-Finsler manifolds. Then we prove that every proper Douglas DWP-Finsler manifold is Riemannian. We show that a proper DWP-manifold is Landsbergian…
Researchers create spectral triples for twisted crossed products using Kasparov's external product.
problem Constructing spectral triples for twisted crossed products.
method Using Kasparov's external product, the construction of spectral triples for twisted crossed products is achieved.
result The construction of spectral triples for twisted crossed products is possible under suitable assumptions.
Paper studies Landsberg curvature of a specific Finsler metric.
problem Analyzing Landsberg curvature of a particular Finsler metric.
method Derived Landsberg curvature and mean Landsberg curvature of the twisted product Finsler metric.
result Necessary and sufficient conditions for the metric to be Landsberg or weakly Landsberg are established.
Study properties of hyperbolic Yamabe solitons in submanifolds.
problem Characterize and understand hyperbolic Yamabe solitons in submanifolds.
method Define hyperbolic Yamabe flow, prove properties, and classify solitons.
result Prove that hyperbolic Yamabe solitons are pseudosymmetric or metallic shaped.
In this paper, we compute the index form of the multiply twisted products. We study the Killing vector fields on the multiply twisted product manifolds and determine the Killing vector fields in some cases. We compute the curvature of the multiply twisted products with a semi-symmetric metric connection and show that t…
Paper proves non-existence of certain Riemannian manifolds.
problem Non-existence of complete twisted and warped products.
method Proves Liouville-type theorems for Riemannian manifolds.
result Generalizes and complements results for compact manifolds.
On the product of two Finsler manifolds M1 M2, we consider the twisted metric F which is construct by using Finsler metrics F1 and F2 on the manifolds M1 and M2, respectively. We introduce horizontal and vertical distributions on twisted product Finsler manifold and study Creducible and semi-C-reducible properties of t…
Legendrian products can be twist spuns under certain conditions.
problem Understanding when Legendrian products are twist spuns.
method Using Legendrian contact homology and augmentation variety analysis.
result Not all Legendrian products are twist spuns.
Study on balanced Hermitian structures on Lie algebras twisted by representations.
problem Conditions for balanced and locally conformally balanced Hermitian structures on Lie algebras.
method Analysis of Hermitian structures on twisted cartesian products of Lie algebras.
result Classification of six-dimensional balanced Hermitian twisted cartesian products Lie algebras.
We characterize Osserman and conformally Osserman Riemannian manifolds with the local structure of a warped product. By means of this approach we analyze the twisted product structure and obtain, as a consequence, that the only Osserman manifolds which can be written as a twisted product are those of constant curvature…
Vanishing Lq,p-cohomology in twisted products.
problem Vanishing Lq,p-cohomology in twisted products. method Generalization of warped products and consideration of q≤p. result Vanishing of the 'middle-dimensional' cohomology.
Study characterizes 2-Killing vector fields on complex spacetimes.
problem Characterize 2-Killing vector fields on multiply twisted product spacetimes. method Determine nonlinear differential equations, find twisted functions, provide solutions, and construct examples.
result Completely describe 2-Killing vector fields and twisted functions on multiply twisted product spacetimes. Given a 3-holed sphere decomposition of an orientable closed surface, it is shown that each orientation preserving homeomorphism of the surface is isotopic to a composition AB where A is a product of positive Dehn twists and B is a product of negative Dehn twists on the decomposition curves.
For 2+1 spacetime dimensions, we derive sufficient conditions for the twisting function in a twisted product spacetime, such that there is a global foliation by spacelike CMC surfaces.
Proposes DR algorithms for distributionally robust off-policy evaluation and learning.
problem Sensitive to environment distribution shifts in offline observational data.
method Doubly robust and distributionally robust approaches for OPE/L.
result Achieves semiparametric efficiency and fast regret rate.
In this paper, we show that the projection of a dualistic structure defined on a twisted product manifold induces dualistic structures on the base and the fiber manifolds, and conversely. Then under some conditions on the Ricci curvature and the Weyl conformal tensor we characterize dually flat structures on twisted pr…
We study doubly-periodic instantons, i.e. instantons on the product of a 1-dimensional complex torus T with a complex line C, with quadratic curvature decay. We determine the asymptotic behaviour of these instantons, constructing new asymptotic invariants. We show that the underlying holomorphic bundle extends to TxP1.…
Estimates latent inner products from an anisotropic Gaussian graph with improved spectral method.
problem Recovering latent inner products from an anisotropic Gaussian random geometric graph.
method Doubly centered adjacency matrix, rank-d spectral approximation, Hermite expansion, decoupling argument.
result Estimator achieves mean squared error rate matching state of the art for isotropic case and ill-conditioned covariance matrices.
This paper computes fixed point Floer cohomology for Dehn twists on surfaces.
problem Computing fixed point Floer cohomology for Dehn twists.
method Developed tools for computing fixed point Floer cohomology and product for Dehn twists in all dimensions.
result Splitting of the product and differential into local and Morse-theoretic contributions.
In this paper we present a certain class of geodesic vector fields of the double-twisted product R X R. Some examples of totally geodesic foliations are given.