Study properties of para-Kähler manifolds with conformal Einstein soliton metrics.
problem Properties of para-Kähler manifolds with conformal Einstein soliton metrics.
method Investigated curvature properties of para-Kähler manifolds admitting conformal Einstein soliton.
result Certain curvature properties of para-Kähler manifolds were studied.
Study properties of Kenmotsu manifolds with conformal η-Einstein soliton metrics.
problem Properties of Kenmotsu manifolds with specific soliton metrics.
method Investigated properties and constructed a 3D example.
result Properties and construction of 3D Kenmotsu manifold with conformal η-Einstein soliton.
Rado's theorem shows all conformal manifolds are paracompact.
problem Paracompactness of conformal manifolds.
method Direct proof using manifold properties.
result Every conformal manifold is paracompact.
Study of *-Conformal η-Ricci soliton on Sasakian manifolds.
problem Characterizing *-Conformal η-Ricci soliton on Sasakian manifolds.
method Analyzing curvature properties and conditions for *-Conformal η-Ricci soliton on Sasakian manifolds.
result Obtained significant results on *-Conformal η-Ricci soliton in Sasakian manifolds under specific curvature conditions.
Boosted conformal procedure improves prediction intervals.
problem Enhancing prediction interval properties like coverage and length.
method Gradient boosting to optimize conformity score function.
result Significant improvements in interval length and coverage.
We study the non-embddability property for a class of real hypersurfaces, called real hypersurfaces of involution type, into the sphere in the low codimensional case, by making use of property of a naturally related Gauss curvature. We also study rigidity problems for conformal maps between a class of Kähler manifolds …
Study indefinite bi-invariant metrics and their conformal properties.
problem Characterize indefinite bi-invariant metrics and their conformal relationships.
method Analyzes Lie algebras under different cases and structures.
result Conformally Einstein properties for various Lie algebras are determined.
We study the basic geometric properties of an indefinite locally conformal Kaehler manifold.
The largest class of Riemannian almost product manifolds, which is closed with respect to the group of the conformal transformations of the Riemannian metric, is the class of the conformal Riemannian P-manifolds. This class is an analogue of the class of the conformal Kähler manifolds in almost Hermitian geometry. The …
We study complex non-Kähler manifolds with Hermitian metrics being locally conformal to metrics with special cohomological properties. In particular, we provide examples where the existence of locally conformal holomorphic-tamed structures implies the existence of locally conformal Kähler metrics, too.
Study on geometric properties of h-conformal semi-invariant submersions.
problem Exploring geometric characteristics of h-conformal semi-invariant submersions.
method Investigation of quaternionic Kähler manifolds and Riemannian manifolds, focusing on integrability of distributions and foliations.
result Established necessary and sufficient conditions for total geodesic submersions and twisted product manifolds.
We are studying the harmonic and twistor equation on Lorentzian surfaces, that is a two dimensional orientable manifold with a metric of signature (1,1). We will investigate the properties of the solutions of these equations and try to relate the conformal invariant dimension of the space of harmonic and twistor spin…
Proves Lorentzian manifold properties for analytic 3D spaces.
problem Analyzing properties of Lorentzian manifolds.
method Analyzes compact, real-analytic, three-dimensional Lorentzian manifolds.
result Identity conformal group preserves metric or manifold is flat.
The paper proves geodesics and conic sections are length-minimizing under specific metrics.
problem Finding shortest paths in complex geometries.
method Calibrations and conformal metrics.
result Geodesics and conic sections are length-minimizing.
Study cohomologies on manifolds with locally conformally symplectic structures.
problem Understanding cohomologies on manifolds with locally conformally symplectic structures.
method Introduced lcs cohomologies, studied elliptic Hodge theory, dualities, and Hard Lefschetz Condition.
result Oeljeklaus-Toma manifolds with precisely one complex place and under an arithmetic condition satisfy the Mostow property.
The note is about some nonlinear curvature conditions which arise naturally in conformal geometry.
The paper characterizes ambient metrics using conformal completion and null infinity properties.
problem Characterizing ambient metrics from a conformal perspective.
method Proving conformal completion and analyzing null infinity properties.
result Identifying conformally covariant conditions to characterize ambient metrics.
This paper provides details of the construction, properties and some applications of the ambient metric associated to a conformal class of metrics on a smooth manifold. Existence and uniqueness of formal expansions defining such metrics are considered. Equivalence with the expansions of associated Poincare metrics is e…
Using Laurent expansions of the Kontsevich-Vishik canonical trace of holomorphic families of classical pseudodifferential operators, we define functionals on the space of Riemannian metrics and investigate their conformal properties, thereby giving a unified description of several conformal invariants and anomalies.
The paper characterizes conformal vector fields in (α,β)-spaces via PDEs.
problem Characterizing conformal vector fields in (α,β)-spaces. method Using partial differential equations (PDEs) to characterize conformal vector fields.
result Properties of conformal vector fields in certain (α,β)-spaces are demonstrated. We find all Ricci semi-symmetric as well as all conformally semi-symmetric spacetimes. Neither of these properties implies the other. We verify that only conformally flat spacetimes can be Ricci semi-symmetric without being conformally semi-symmetric and show that only vacuum spacetimes and spacetimes with just a Λ-t…
Unique continuation results are proved for metrics with prescribed Ricci curvature in the setting of bounded metrics on compact manifolds with boundary, and in the setting of complete, conformally compact metrics. Related to this issue, an isometry extension property is proved: continuous groups of isometries at confor…
The paper examines curvature properties of a specific magnetic spacetime metric.
problem Investigating the geometric properties of Melvin magnetic spacetime metric.
method Analyzing a Melvin type static, cylindrically symmetric spacetime metric in Weyl form, considering curvature conditions and tensor properties.
result The Melvin magnetic metric is pseudosymmetric and satisfies the Roter type condition.
We prove the unique continuation property at the conformal infinity for asymptotically hyperbolic Einstein metrics.
The paper extends fractional Laplacian theory using symmetric spaces and extension problems.
problem Developing a new framework for fractional Laplacians.
method Using representation theory on symmetric spaces and extension problems.
result Constructed new boundary operators with conformal properties.
Study on conformal deformations of complex Finsler metrics.
problem Characterization and stability of Kähler Finsler metrics.
method Characterization and study of critical points in conformal classes.
result Stability of critical Kähler Finsler metrics obtained.
New adaptive conformal predictive systems developed.
problem Severe restrictions on adapting predictive distributions to test objects.
method Calibrating existing predictive systems to ensure full adaptability and validity.
result Developed fully adaptive split-conformal and cross-conformal predictive systems.
The paper explores properties of LCK spaces and their coverings.
problem Understanding the structure and properties of LCK spaces and their coverings.
method Proving that a space is LCK if and only if its universal cover is Kähler, and showing that a complex space with discrete fibers over an LCK space also has an LCK structure.
result Spaces with discrete fibers over LCK spaces also have LCK structures.
The paper studies conformally flat cubic metrics with isotropic curvature, finding they must be Minkowski.
problem Understanding conformal properties of cubic metrics with isotropic scalar curvature.
method Analyzing the conformal flatness and isotropic scalar curvature of cubic metrics.
result Cubic metrics with weakly isotropic scalar curvature must be Minkowski metrics.
Motivated by the study of Weyl structures on conformal manifolds admitting parallel weightless forms, we define the notion of conformal product of conformal structures and study its basic properties. We obtain a classification of Weyl manifolds carrying parallel forms, and we use it to investigate the holonomy of the a…
We study conformal Spin-subgeometry of submanifolds in a semi-Riemannian Spin-manifold, focusing on conformal Spin-manifolds (M,[h]) and their Poincaré-Einstein metrics (X,g+). Our approach is based on the spectral theory of Dirac operator in the ambient Spin-manifold, and associated spinor valued meromorp…
The paper explores curvature properties of specific metric spaces.
problem Investigating curvature properties of Cartan spaces with mth root metrics.
method Analyzing isotropic mean Berwald and Landsberg curvatures, and examining conformal β-changes.
result Conditions for conformal β-change of m-th root metrics to be locally dually flat and locally Minkowskian.
Classifies non-Kahler surfaces and proves local conformal Kahler property.
problem Classifying non-Kahler surfaces and understanding their geometric properties.
method Proof based on Buchdahl-Lamari theorem.
result All non-Kahler surfaces that are not of class VII are locally conformally Kahler.
Study curvature properties in special manifolds using specific tensors.
problem Investigate curvature conditions in 2-quasi-Einstein manifolds.
method Analyze Riemann-Christoffel curvature tensor and its linear combinations with Ricci tensor.
result Satisfy pseudosymmetry type curvature conditions in certain manifolds.
Validates conformal prediction for network data under non-uniform sampling.
problem Validity of conformal prediction for network data under non-representative sampling.
method Interprets sampling mechanisms as selection rules, studies validity conditional on selection events, uses permutation invariance and joint exchangeability.
result Finite-sample validity of conformal prediction for certain selection events and asymptotic validity for random walk sampling.
The paper proposes a method to align AI models using conformal risk control.
problem Aligning AI models to meet end-user requirements in non-generative settings.
method Post-processing a pre-trained model to better align with a subset of functions using conformal risk control.
result A probabilistic guarantee that the resulting conformal interval around a model contains a function approximately satisfying a desired property.
Study eigenvalues of conformal Laplacian under Sire-Xu normalization.
problem Existence and properties of extremal eigenvalues under a specific normalization.
method Variational analysis of eigenvalue functional under Sire-Xu normalization.
result Necessary conditions and existence results for extremal eigenvalues.
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.
Unified study of nine multi-output conformal methods with generalized scores.
problem Challenges in extending conformal prediction to multi-output problems.
method Nine conformal methods with generalized multi-output conformity scores.
result Generalized scores ensure asymptotic conditional coverage and exact finite-sample marginal coverage.
New definition for a special type of complex manifolds.
problem Characterizing compact locally conformally hyperkähler manifolds.
method Equivalent definition using a nondegenerate complex two-form.
result Established a conformal analogue of Beauville's theorem.
We present an overview of recent results in locally conformally Kähler geometry, with focus on the topological properties which obstruct the existence of such structures on compact manifolds.
The purpose of the present paper is to study the differential geometric properties of a quaternion CR-submanifold in a locally conformal quaternion Kaehler manifold.
The study characterizes surfaces with specific harmonic properties in pseudo-conformal geometry.
problem Characterizing surfaces with harmonic properties in pseudo-conformal geometry.
method Investigating sphere congruences, quasi-umbilical surfaces, and constant mean curvature surfaces.
result Generically, Bryant's quartic differential is divergence free if and only if the surface is superconformal or orthogonal to a harmonic congruence of spheres.
In this paper, we consider the problem of building a conformal boundary, embedding a pseudo-Riamnnian manifold as an open subset of a bigger one. We get first results about conformal maximality. We also show that in dimension ≥3, there are rigidity properties for the topological boundary of such a conformal embed…
Paper studies solutions to a specific equation in conformal geometry with singular sets.
problem Singular solutions to a fully non-linear equation in conformal geometry.
method Uses a classical gluing method adapted to the fully non-linear setting.
result Shows the classical gluing method can be applied to the σ2--Yamabe equation. Reviews recent work on biharmonic conformal maps and their properties.
problem Understanding biharmonic conformal maps and their properties.
method Analyzes recent research on biharmonic conformal maps, immersions, and maps between manifolds.
result Links biharmonic conformal maps to isoparametric functions and Yamabe type equations.
We study the conformal geometry of timelike curves in the (1+2)-Einstein universe, the conformal compactification of Minkowski 3-space defined as the quotient of the null cone of R2,3 by the action by positive scalar multiplications. The purpose is to describe local and global conformal invariants of time…
Differentially private conformal prediction improves statistical efficiency.
problem Quantifying uncertainty in private data analysis.
method Introducing differential conformal prediction and developing Differentially Private Conformal Prediction (DPCP).
result DPCP produces tighter prediction sets than existing private split conformal approaches.