arXiv research

In this paper, we introduce and investigate a general transformation or change of Finsler metrics, which is referred to as a generalized $β$-conformal change: $L(x,y) \longrightarrow\overline{L}(x,y) = f(e^{σ(x)}L(x,y),β(x,y)).$ This transformation combines both $β$-change and conformal change in a general setting. T…

We investigate what we call a conformal $β$ - change in Finsler spaces, namely $L(x,y)\to ~^{\ast}L(x,y)=e^{σ(x)}L(x,y)+β(x,y)$ where~$σ~$ is a function of $x~ only ~and ~ β(x, y)$ is a given 1- form. This change generalizes various types of changes: conformal changes, Randers changes and $β$ - changes. Under this c…

In the year 1984 Shibata investigated the theory of a change which is called a $β$-change of a Finsler metric. On the other hand in 1985 a systematic study of geometry of hypersurfaces in Finsler spaces was given by Matsumoto. In the present paper is to devoted to the study of a condition for a Randers conformal chang…

On a Finsler manifold $(M,L)$, we consider the change $L\longrightarrow\bar{L}(x,y)=e^{σ(x)}L(x,y)+β(x,y)$, which we call a $β$-conformal change. This change generalizes various types of changes in Finsler geometry: conformal, $C$-conformal, $h$-conformal, Randers and generalized Randers changes. Under this change, we …

Study on special anisotropic conformal changes of conic pseudo-Finsler surfaces.

New method detects changes in data streams efficiently.

The paper studies anisotropic conformal changes in pseudo-Finsler surfaces.

In this paper, we investigate the change of Finslr metrics $L(x,y) \to\bar{L}(x,y) = f(e^{σ(x)}L(x,y),β(x,y)),$ which we refer to as a generalized $β$-conformal change. Under this change, we study some special Finsler spaces, namely, quasi C-reducible, semi C-reducible, C-reducible, $C_2$-like, $S_3$-like and $S_4$-l…

Plane Delaunay triangulations are rigid under Luo's discrete conformal change.

Motivation: Proteins are known to undergo conformational changes in the course of their functions. The changes in conformation are often attributable to a small fraction of residues within the protein. Therefore identification of these variable regions is important for an understanding of protein function. Results: We …

Conformal Test Martingales can be 'blind' to significant changes in data distribution.

The present paper is a continuation of a foregoing paper [Tensor, N. S., 69 (2008), 155-178]. The main aim is to establish \emph{an intrinsic investigation} of the conformal change of the most important special Finsler spaces, namely, $C^{h}$-recurrent, $C^{v}$-recurrent, $C^{0}$-recurrent, $C_{2}$-like, quasi-$C$-redu…

Singular Yamabe problems involve changing sign solutions with interesting geometric properties.

We study infinitesimal conformal deformations of a triangulated surface in Euclidean space and investigate the change in its extrinsic geometry. A deformation of vertices is conformal if it preserves length cross-ratios. On one hand, conformal deformations generalize deformations preserving edge lengths. On the other h…

A conformal change of $TM\oplus T^*M$ is a morphism of the form $(X,α)\mapsto(X,e^τα)$ $(X\in TM,α\in T^*M,τ\in C^\infty(M))$. We characterize the generalized almost complex and almost Hermitian structures that are locally conformal to integrable and to generalized Kähler structures, respectively, and give examples of …

Plane triangulations remain rigid under discrete conformal changes.

New method detects data distribution changes and retraining is advised.

Study identifies obstructions for solving a 4th-order boundary problem.

Unified theoretical guarantees for distribution-free changepoint detection and testing.

Paper proves geodesics and focal points unchanged by conformal changes in pseudo-Finsler manifolds.

The paper explores curvature properties of specific metric spaces.

This research examines anisotropic conformal transformations of pseudo-Finsler surfaces.

Study on pseudo-Einstein 3-manifolds, calculating determinant changes under conformal transformations.

Spectral Adaptive Conformal Prediction for Structured Non-Exchangeable Data

Develops PromptShift-CRC for drift-aware conformal risk control in foundation models under prompt and domain shift.

The aim of the present paper is to investigate conformal changes in absolute parallelism geometry. We find out some new conformal invariants in terms of the Weitzenböck connection and the Levi-Civita connection of an absolute parallelism space.

The aim of the present paper is to establish a global theory of conformal changes in Finsler geometry. Under this change, we obtain the relationships between the most important geometric objects associated to $(M,L)$ and the corresponding objects associated to $(M,\tilde{L})$, $\widetilde{L}=e^{σ(x)} L$ being the Finsl…

CAT(0) spaces can be deformed in various ways.

Study describes how conformal metrics behave as Q-curvature changes, forming spherical bubbles.

Constructs conformal boundary operators and fractional Laplacians.

We compute renormalized curvature integrals on Poincaré-Einstein manifolds.

We construct a new class of biharmonic maps, which are the critical points for the bienergy functional, by deforming conformally the codomain metric of harmonic Riemannian submersions such that they become nonharmonic but biharmonic.

In this paper, we prove a classification theorem of 4-manifolds according to some conformal invariants, which generalizes the conformally invariant sphere theorem of Chang-Gursky-Yang \cite{CGY}. Moreover, it provides a four-dimensional analogue of the well-known classification theorem of Schoen-Yau \cite{SY2} on 3-man…

The paper extends the study of conformally flat spaces to four dimensions.

Python library for conformal prediction, licensed under MIT.

Online method selects candidates from data streams, ensuring irreversible decisions.

Researchers solve the negative Yamabe case for scalar curvature prescription.

Here, by extending the definition of circle to Finsler geometry, we show that, every circle-preserving local diffeomorphism is conformal. This result implies that in Finsler geometry, the definition of concircular change of metrics, a priori, does not require the conformal assumption.

This paper studies conformal biharmonic immersions. We first study the transformations of Jacobi operator and the bitension field under conformal change of metrics. We then obtain an invariant equation for a conformal biharmonic immersion of a surface into Euclidean 3-space. As applications, we construct a 2-parameter …

The behavior under conformal change of the renormalized volume coefficients associated to a pseudo-Riemannian metric is investigated. It is shown that they define second order fully nonlinear operators in the conformal factor whose algebraic structure is elucidated via the introduction of "extended obstruction tensors"…

The study of rigidity theorems on 4-manifolds with boundary.

Survey on LCK structures on solvmanifolds, focusing on invariant and Vaisman structures.

Physical reasons suggested in \cite{Ha-Ha} for the \emph{Quantum Gravity Problem} lead us to study \emph{type-changing metrics} on a manifold. The most interesting cases are \emph{Transverse Riemann-Lorentz Manifolds}. Here we study the conformal geometry of such manifolds.

Investigates max width of unit volume 3-spheres in conformal classes.

This paper offers a distribution-free method for post-detection changepoint localization.

CROC identifies the earliest-changing stream as the root cause in multi-stream data.

The paper addresses the reliability of conformal prediction under covariate shift.

CASCADE improves uncertainty communication in Parkinson's disease medication management.