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Strong Hamel functions and symmetries

Ioan Bucataru, Georgeta Cretu

Abstract

A strong Hamel function is a Hamel function that is the geodesic derivative of some 0-homogeneous function. We prove that strong Hamel functions induce dual symmetries and dynamical symmetries and provide the conditions such that these symmetries are induced by strong Hamel functions. We show that projective deformations by strong Hamel functions preserve the $χ$-curvature and analyse the relationship with some other functions (Funk and weak Funk functions) preserving curvature tensors under projective deformations. In the flat case, any Hamel function is a strong Hamel function.

Strong Hamel functions and symmetries

Abstract

A strong Hamel function is a Hamel function that is the geodesic derivative of some 0-homogeneous function. We prove that strong Hamel functions induce dual symmetries and dynamical symmetries and provide the conditions such that these symmetries are induced by strong Hamel functions. We show that projective deformations by strong Hamel functions preserve the -curvature and analyse the relationship with some other functions (Funk and weak Funk functions) preserving curvature tensors under projective deformations. In the flat case, any Hamel function is a strong Hamel function.
Paper Structure (5 sections, 8 theorems, 36 equations)

This paper contains 5 sections, 8 theorems, 36 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Strong Hamel functions
  4. Strong Hamel functions and symmetries
  5. $\chi$-curvature and strong Hamel functions

Key Result

Lemma 3.2

The Euler-Lagrange $1$-form EL is a projective invariant, when restricted to $1$-homogeneous functions. The class of Hamel functions and strong Hamel functions are preserved by projective deformations.

Theorems & Definitions (21)

  • Definition 2.1
  • Remark 2.2
  • Definition 3.1
  • Lemma 3.2
  • proof
  • Lemma 3.3
  • proof
  • Lemma 3.4
  • proof
  • Definition 4.1
  • ...and 11 more