Characterizes warping functions in Einstein Poisson warped spaces.
problem Existence and nonexistence of warping functions with constant scalar curvature.
method Analyzes various dimensions of base space and constant scalar curvature conditions.
result Characterizes warping functions for different dimensions of base space.
Optimizes dynamic time warping for better signal alignment.
problem Aligning signals with dynamic time warping.
method Formulates as an optimal control problem, discretizes, and uses dynamic programming.
result High accuracy warping function achieved in few iterations.
The article surveys recent results on warped and CR-warped product submanifolds in Kaehler manifolds.
problem Characterizing submanifolds in Kaehler manifolds using warped and CR-warped products.
method Analyzing properties of warped and CR-warped products in the context of Kaehler manifolds.
result Presented several results on the geometry of warped and CR-warped product submanifolds.
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.
Generalizes warped product submersion to conformal case.
problem Understanding angles preservation in submersions.
method Introduces conformal warped product submersion.
result Fundamental tensors derived for conformal submersion.
Proves a theorem for a specific type of warped product space.
problem Analyzing warped product spaces.
method Uses the warped function \( f(r) = \cosh\left(r\sqrt{\frac{\lambda}{n-2}}
ight) \) to prove the theorem.
result Proves an almost splitting theorem for the specified warped product space.
The paper explores geometric properties of Riemannian warped product maps and their curvature.
problem Investigating the geometric properties of Riemannian warped product maps.
method The approach involves establishing conditions for geodesics, deriving curvature tensors, and examining various types of maps.
result Derivation of integral formula for scalar curvature of conformal Riemannian warped product maps.
Study shows how certain metrics can be split into warped products.
problem Understanding conditions under which metrics can be split as warped products.
method Investigating warped area-minimizing hypersurfaces and spectral Ricci/scalar curvature bounds.
result Metrics can be locally split as warped products under specific curvature conditions.
The paper proves rigidity for submanifolds in warped product manifolds.
problem Rigidity of submanifolds in warped product manifolds.
method Dihedral extremality and rigidity theorem for submanifolds with polyhedral boundary.
result Dihedral rigidity results for hyperbolic polyhedra in flat warped product spaces.
Study on warped product Yamabe solitons with constant fiber curvature.
problem Characterizing nontrivial warped product Yamabe gradient solitons.
method Investigation of warped product manifolds, derivation of scalar curvature estimates.
result Nontrivial warped product Yamabe gradient solitons have constant scalar curvature in the fiber.
The paper explores warped-like product metrics with exceptional holonomy groups.
problem Exploring new metrics with exceptional holonomy groups.
method Presented a general ansatz of warped-like product metric and studied specific examples.
result Explicit examples of (3+3+2) and (3+3+1) warped-like product manifolds with Spin(7) and G2 holonomy, respectively. The warping matrix has been defined for knot projections and knot diagrams by using warping degrees. In particular, the warping matrix of a knot diagram represents the knot diagram uniquely. In this paper we show that the rank of the warping matrix is one greater than the crossing number. We also discuss the linearly i…
We prove that complete warped product Einstein metrics with isometric bases, simply connected space form fibers, and the same Ricci curvature and dimension are isometric. In the compact case we also prove that the warping functions must be the same up to scaling, while in the non-compact case there are simple examples …
This paper finds all prime alternating knots with minimal warping degree two.
problem Finding knots with minimal warping degree.
method Examined all prime alternating knots and determined those with minimal warping degree two.
result All prime alternating knots with minimal warping degree two were identified.
Warped product affects divergences in information geometry.
problem Warped product's impact on divergences in information geometry.
method Study of warped product on information geometry.
result Warped product does not preserve canonical divergences.
Study properties of bi-warped product submanifolds in specific geometric spaces.
problem Characterize geometric properties of bi-warped product submanifolds.
method Analyze squared norm of second fundamental form and warping functions.
result Relationship between squared norm and warping functions for proper slant submanifolds.
Study new warped metrics with vanishing Douglas curvature.
problem Warped product metrics and their curvature properties.
method Solve differential equation for vanishing Douglas curvature.
result Classify Douglas warped product metrics.
Sharp growth estimates for warping functions in warped product manifolds.
problem Estimating growth of warping functions in warped product manifolds.
method Applying an average method in PDE to establish sharp inequalities.
result Sharp inequalities between mean curvature and sectional curvatures of the ambient manifold.
New rigidity found for 3D warped product domains.
problem Finding rigidity conditions for warped product domains.
method Developed scalar curvature rigidity for a general class of domains.
result Identified domains satisfying a boundary condition analogous to logarithmic concavity.
The paper modifies a warped product space to find conditions for constant height functions.
problem Finding sufficient conditions for the height function to be constant in a modified warped product space.
method The paper modifies the warped product space by adding a warping function and discusses the sufficient condition for the height of immersed surfaces.
result The paper establishes a sufficient condition for the height function to be constant in the modified warped product space.
The paper explores Einstein warped G2 and Spin(7) manifolds.
problem Understanding Einstein warped G2 and Spin(7) manifolds.
method Warped G2 and Spin(7) structures with Einstein fiber are studied.
result Explicit descriptions of torsion forms for these structures.
Characterizes knots with warping sum ≤ 3 and provides some knots with warping sum 4.
problem Understanding the warping sum of knots and its constraints.
method Characterization and example provision of knots based on their warping sum.
result Knots with warping sum ≤ 3 are characterized, and some knots with warping sum 4 are identified.
Paper defines and studies Clairaut warped product Riemannian maps.
problem Understanding the geometry of specific Riemannian maps.
method Identify geodesic conditions, derive conditions for Clairaut maps, and calculate curvature.
result Found conditions for a warped product Riemannian map to be Clairaut.
The paper computes fundamental groups of warped cones and finds expanders.
problem Understanding the fundamental groups of warped cones.
method Computing discrete fundamental groups of warped cones.
result Warped cones can be coarsely non-equivalent to box spaces.
Study on warped product pointwise semi-slant submanifolds in Sasakian and cosymplectic manifolds.
problem Investigate the geometry of pointwise semi-slant submanifolds and their warped products.
method Using the notion of pointwise slant submanifolds, investigate the geometry of pointwise semi-slant submanifolds and their warped products in Sasakian and cosymplectic manifolds.
result Prove the existence of no proper pointwise semi-slant warped product submanifolds other than contact CR-warped products in Sasakian manifolds.
Optimal warping paths are unique for almost every pair of time series.
problem Adverse effects in learning due to non-unique optimal warping paths.
method Assumption of squared error local costs, measure-theoretic analysis.
result Optimal warping paths are unique almost everywhere.
Study Einstein warped products with Einstein base and fiber.
problem Characterize Einstein warped products with Einstein base and fiber.
method Investigate necessary and sufficient conditions for a warped product to be Einstein.
result Explicitly determine the warping function when the base is hyperbolic space.
Conditions for flat 3-manifolds with diagonal metrics are identified.
problem Characterizing flat 3-manifolds with diagonal metrics.
method Provided necessary and sufficient conditions for flatness.
result Characterized flat manifolds of warped product-type.
In this paper, we generalize the geometry of the product pseudo-Riemannian manifold equipped with the product Poisson structure (\cite{Nas2}) to the geometry of a warped product of pseudo-Riemannian manifolds equipped with a warped Poisson structure. We construct three bivector fields on a product manifold and show tha…
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.
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.
Inverse mean curvature flows studied in warped product manifolds with positive warping factor.
problem Analyzing inverse mean curvature flows in warped product manifolds.
method Investigating starshaped, mean convex hypersurfaces in warped product manifolds with positive warping factor.
result Existence and properties of inverse mean curvature flows in warped product manifolds with positive warping factor.
Study on warped products in contact skew-CR submanifolds with inequality and examples.
problem Analyzing warped products in contact skew-CR submanifolds.
method Established an inequality for the squared norm of the second fundamental form.
result Derived inequality and provided non-trivial examples.
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.
In this paper we study the space of solutions to an overdetermined linear system involving the Hessian of functions. We show that if the solution space has dimension greater than one, then the underlying manifold has a very rigid warped product structure. We obtain a uniqueness result for prescribing the Ricci curvatur…
A new warping-invariant distance improves nearest-neighbor classification efficiency.
problem dtw distance inconsistency and inefficiency in nearest-neighbor classification.
method Showed dtw is not warping-invariant, converted to twi distance.
result twi distance equivalent error rates to dtw, more efficient.
Study of warped product pointwise bi-slant submanifolds in Kaehler manifolds.
problem Characterize warped product pointwise bi-slant submanifolds in Kaehler manifolds.
method Extends previous studies on warped product slant submanifolds.
result Extends several important results on warped product slant submanifolds.
We derive one unified formula for Ricci curvature tensor on arbitrary warped product manifold by introducing a new notation for the lift vector and the Levi-Civita connection.This formula is helpful to further consider Ricci flow (RF) and hyperbolic geometric flow (HGF) and evolution equations on warped product manifol…
Study investigates concircular curvature on warped products.
problem Effects of concircular flatness and symmetry on fibre and base manifolds.
method Investigated concircular flat and symmetric warped product manifolds, considered divergence free curvature tensor.
result Results applied to generalized Robertson-Walker and static space-times.
The study examines properties of gradient Yamabe solitons on warped product manifolds.
problem Investigating properties of gradient Yamabe solitons on warped product manifolds.
method Utilizing the maximum principle and modified Li-Yau's technique, the study finds gradient estimates for the warping function.
result The study finds three different gradient estimates for the warping function, one for each sign of the scalar curvature of the fiber manifold.
Study on new warped product submanifolds in para-Kähler manifolds.
problem Exploring new types of submanifolds in para-Kähler manifolds.
method Introducing and analyzing PR-pseudo-slant warped product submanifolds. result Existence and non-existence results for PR-pseudo-slant warped product submanifolds. Characterizes Ricci almost solitons on semi-Riemannian warped products.
problem Characterizing Ricci almost solitons on semi-Riemannian warped products.
method Characterization using potential function dependence and fiber properties.
result Fiber is necessarily an Einstein manifold; base and warped product are also Einstein manifolds under certain conditions.
A new GP model for non-Gaussian data with explicit inverse warping.
problem Limited expressiveness and computational complexity of Gaussian processes for non-Gaussian data.
method Compositionally-warped Gaussian processes (CWGP) with explicit inverse warping.
result CWGP provides more accurate predictions and shorter computation times than traditional warped GPs.
In this paper, we study the Einstein warped products and multiply warped products with a quarter-symmetric connection. We also study warped products and multiply warped products with a quarter-symmetric connection with constant scalar curvature. Then apply our results to generalized Robertson-Walker spacetimes with a q…
The study finds lower bounds for the warping degree of a knot projection.
problem Determining the warping degree of a knot projection.
method Examining the maximal number of regions sharing no crossings for a fixed crossing in a knot projection.
result Lower bounds for the warping degree of a knot projection are provided.
In this paper we study the warped product submanifolds of a Lorentzian paracosymplectic manifold and obtain some nonexistence results. We show that a warped product semi-invariant submanifold in the form {M=MT×fM⊥} of Lorentzian paracosymplectic manifold such that the characteristic vector field is n…
Study on rigidity of warped cones and expanders.
problem Coarse geometry of warped cones and expanders.
method Use of coarse topology for warped cones, including computation of coarse fundamental groups.
result Rigidity theorem for coarse geometry of warped cones.
Study optimal inequality for contact CR-warped product submanifolds in cosymplectic space forms.
problem Optimal inequality for contact CR-warped product submanifolds in cosymplectic space forms.
method Using Gauss and Codazzi equations, prove an optimal inequality.
result Prove an optimal inequality for contact CR-warped product submanifolds.