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arXiv · 1708.09375

Geometric features of Vessiot--Guldberg Lie algebras of conformal and Killing vector fields on $\mathbb{R}^2$

M. M. Lewandowski·J. de Lucas
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Abstract

This paper locally classifies finite-dimensional Lie algebras of conformal and Killing vector fields on $\mathbb{R}^2$ relative to an arbitrary pseudo-Riemannian metric. Several results about their geometric properties are detailed, e.g. their invariant distributions and induced symplectic structures. Findings are illustrated with two examples of physical nature: the Milne--Pinney equation and the projective Schrödinger equation on the Riemann sphere.

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M. M. Lewandowski, J. de Lucas. 2017-08-30. Geometric features of Vessiot--Guldberg Lie algebras of conformal and Killing vector fields on $\mathbb{R}^2$. https://doi.org/10.4064/bc113-0-13

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