arXiv research

The paper studies T-tensor of spherically symmetric Finsler metrics and characterizes metrics satisfying the T-condition.

In this paper, we study the long existence problem of non Berwaldian Landsberg spaces using the conformal transformation point of view. Under conformal transformation, the Berwald and Landesberg tensors are calculated in terms of the T-tensor. By giving examples, we show that under conformal transformation, there are L…

We describe the $(α,β)$-metrics whose the $T$-tensor vanishes ($T$-condition) and the $(α,β)$-metrics that satisfy the $σT$-condition $σ_hT^h_{ijk}=0$, where $σ_h=\frac{\partial σ}{\partial x^h}$ and $σ$ is a smooth function on $M$. These classes have already been obtained by Z. Shen and G. S. Asanov in a completely di…

The study classifies quasi-Einstein manifolds with constant scalar curvature.

The paper classifies Finsler surfaces satisfying the T-condition or σT-condition.

The aim of this paper is to expose some geometrical properties of the locally Minkowski-Cartan space with the Berwald-Moor metric of momenta. This space is regarded as a particular case of the $m$-th root Cartan space. Thus, Section 2 studies the $v$-covariant derivation components of the $m$-th root Cartan space. Sect…

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…

We provide a novel analysis of low-rank tensor completion based on hypergraph expanders. As a proxy for rank, we minimize the max-quasinorm of the tensor, which generalizes the max-norm for matrices. Our analysis is deterministic and shows that the number of samples required to approximately recover an order-$t$ tensor…

We study low rank matrix and tensor completion and propose novel algorithms that employ adaptive sampling schemes to obtain strong performance guarantees. Our algorithms exploit adaptivity to identify entries that are highly informative for learning the column space of the matrix (tensor) and consequently, our results …

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