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We construct a theory in which the gravitational interaction is described only by torsion, but that generalizes the Teleparallel Theory still keeping the invariance of local Lorentz transformations in one particular case. We show that our…
In this work we investigate analytic static and spherically symmetric solutions of a generalized theory of gravity in the Einstein-Cartan formalism. The main goal consists in analyzing the behavior of the solutions under the influence of a…
Teleparallel gravity, a gauge theory for the translation group, turns up as fully equivalent to Einstein's general relativity. In spite of this equivalence, it provides a whole new insight into gravitation. It breaks several paradigms…
In this paper, Lie symmetry group method is applied to find the lie point symmetries group of a PDE system that is determined general form of four-dimensional Einstein Walker manifold. Also we will construct the optimal system of…
We investigate some topological properties of random geometric complexes and random geometric graphs on Riemannian manifolds in the thermodynamic limit. In particular, for random geometric complexes we prove that the normalized counting…
Handling symmetries in optimization problems is essential for devising efficient solution methods. In this article, we present a general framework that captures many of the already existing symmetry handling methods. While these methods are…
We review the current status of Finsler-Lagrange geometry and generalizations. The goal is to aid non-experts on Finsler spaces, but physicists and geometers skilled in general relativity and particle theories, to understand the crucial…
We apply thermodynamics method to generate exact solution with maximum symmetric surface for Einstein equation without solving it. The exact solutions are identified with which people have solved before. The horizons structure of solutions…
For interacting classical field theories such as general relativity exact solutions typically can only be found by imposing physically motivated (Killing) {\it symmetry} assumptions. Such highly symmetric solutions are then often used as…
Various tasks in scientific computing can be modeled as an optimization problem on the indefinite Stiefel manifold. We address this using the Riemannian approach, which basically consists of equipping the feasible set with a Riemannian…
The notion of $\Gamma$-symmetric space is a natural generalization of the classical notion of symmetric space based on $\Z_2$-grading of Lie algebras. In our case, we consider homogeneous spaces $G/H$ such that the Lie algebra $\g$ of $G$…
In this paper we consider an inverse problem of determining a minimal surface embedded in a Riemannian manifold. We show under a topological condition that if $\Sigma$ is a $2$-dimensional embedded minimal surface, then the knowledge of the…
In this paper we combine many of the standard and more recent algebraic techniques for testing isomorphism of finite groups (GpI) with combinatorial techniques that have typically been applied to Graph Isomorphism. In particular, we show…
We study two aspects of the loop group formulation for isometric immersions with flat normal bundle of space forms. The first aspect is to examine the loop group maps along different ranges of the loop parameter. This leads to various…
The purpose of this paper is to present for the first time an elementary summary of a few recent results obtained through the application of the formal theory of partial differential equations and Lie pseudogroups in order to revisit the…
A generalized symmetry of a system of differential equations is an infinitesimal transformation depending locally upon the fields and their derivatives which carries solutions to solutions. We classify all generalized symmetries of the…
Any representation of data involves arbitrary investigator choices. Because those choices are external to the data-generating process, each choice leads to an exact symmetry, corresponding to the group of transformations that takes one…
This thesis is devoted to algorithmic aspects of the implementation of Cartan's moving frame method to the problem of the equivalence of submanifolds under a Lie group action. We adopt a general definition of a moving frame as an…
Given dense image feature correspondences of a non-rigidly moving object across multiple frames, this paper proposes an algorithm to estimate its 3D shape for each frame. To solve this problem accurately, the recent state-of-the-art…
We characterize the combinatorial types of symmetric frameworks in the plane that are minimally generically symmetry-forced infinitesimally rigid when the symmetry group consists of rotations and translations. Along the way, we use tropical…