相关论文: Parallel translations for a left invariant spray

This paper examines the geometry of left-invariant vector fields on five-dimensional, simply connected, nilpotent Lie groups equipped with left-invariant Riemannian metrics. Using the canonical identification between the Lie algebra and the…

A result from Gromov ensures the existence of a contact structure on any connected non-compact odd dimensional Lie group. But in general such structures are not invariant under left translations of the Lie group. The problem of finding…

We consider the nonlinear problem of determining a connection and a Higgs field from the corresponding parallel transport along geodesics on a Riemannian manifold with boundary, in any dimension. The problem can be reduced to an integral…

Horizontal endomorphisms, almost complex structures, vertical, horizontal and complete lifts on prolongation of a Lie algebroid are considered. Then using exact sequences, semisprays are constructed. Moreover, important geometrical objects…

The Finsleroid-Finsler space is constructed over an underlying Riemannian space by the help of a scalar $g(x)$ and an input 1-form $b$ of unit length. Explicit form of the entailed tensors, as well as the respective spray coefficients, is…

We study the geometry of Lie groups $G$ with a continuous Finsler metric, assuming the existence of a subgroup $K$ such that the metric is right-invariant for the action of $K$. We present a systematic study of the metric and geodesic…

We study a nonlinear system of partial differential equations which describe rotating shallow water with an arbitrary constant polytropic index $\gamma $ for the fluid. In our analysis we apply the theory of symmetries for differential…

Methods for the design of physical parameterization schemes that possess certain invariance properties are discussed. These methods are based on different techniques of group classification and provide means to determine expressions for…

In this work, Lie symmetry analysis is performed on a coupled nonlinear cross-diffusion system with varying cross-section geometry. The system describes two interacting quantities whose material properties, namely the capacity functions and…

In this paper we consider simply connected Lie groups equipped with left invariant Randers metrics which arise from left invariant Riemannian metrics and left invariant vector fields. Then we study the intersection between automorphism and…

The main purpose of this article is to introduce a comprehensive, unified theory of the geometry of all connections. We show that one can study a connection via a certain, closely associated second-order differential equation. One of the…

Left-invariant optimal control problems on Lie groups form an important class of problems with big symmetry group. They are interesting from the theoretical point of view since they often can be completely studied, and general features can…

We investigate contact Lie groups having a left invariant Riemannian or pseudo-Riemannian metric with specific properties such as being bi-invariant, flat, negatively curved, Einstein, etc. We classify some of such contact Lie groups and…

In the present paper, the flag curvature of invariant Randers metrics on homogeneous spaces and Lie groups is studied. We first give an explicit formula for the flag curvature of invariant Randers metrics arising from invariant Riemannian…

In this paper, we formulate a procedure to obtain a generalization of Milnor frames for left-invariant pseudo-Riemannian metrics on a given Lie group. This procedure is an analogue of the recent studies on left-invariant Riemannian metrics,…

This is a short presentation of some classical results on finite dimensional complex Lie algebras (classification of nilpotent Lie algebras, deformations and perturbations, contractions and rigidity). We present some applications to…

In this paper we are investigating variational homogeneous second order differential equations by considering the questions of how many different variational principles exist for a given spray. We focus our attention on h(2)-variationality;…

Let $G$ be a connected, simply connected, nilpotent Lie group whose irreducible unitary representations are square-integrable modulo the center. We obtain characterization results for reproducing formulas associated with the left…

In this paper we investigate the relations between semispray, nonlinear connection, dynamical covariant derivative and Jacobi endomorphism on Lie algebroids. Using these geometric structures, we study the symmetries of second order…

In this paper, firstly we study some left invariant Riemannian metrics on para-hypercomplex 4-dimensional Lie groups. In each Lie group, the Levi-Civita connection and sectional curvature have been given explicitly. We also show these…