Two-dimensional metrics admitting precisely one projective vector field
Vladimir S. Matveev
TL;DR
This paper provides a comprehensive classification of two-dimensional metrics that admit a unique essential projective vector field, solving a problem posed by Sophus Lie in 1882.
Contribution
It offers a complete list of such metrics, addressing a long-standing mathematical question about projective symmetries in 2D geometry.
Findings
Complete classification of 2D metrics with a unique essential projective vector field
Resolution of a problem posed by Sophus Lie in 1882
Advances understanding of projective symmetries in differential geometry
Abstract
We give a complete list of two-dimensional metrics that admit an essential projective vector field. This solves a problem explicitly posed by Sophus Lie in 1882.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Geometry and complex manifolds