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A solution of a problem of Sophus Lie: Normal forms of two-dimensional metrics admitting two projective vector fields

Publication ,  Journal Article
Bryant, RL; Manno, G; Matveev, VS
Published in: Mathematische Annalen
2008

We give a complete list of normal forms for the two-dimensional metrics that admit a transitive Lie pseudogroup of geodesic-preserving transformations and we show that these normal forms are mutually non-isometric. This solves a problem posed by Sophus Lie. © 2007 Springer-Verlag.

Duke Scholars

Published In

Mathematische Annalen

DOI

ISSN

0025-5831

Publication Date

2008

Volume

340

Issue

2

Start / End Page

437 / 463

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics
 

Citation

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Bryant, R. L., Manno, G., & Matveev, V. S. (2008). A solution of a problem of Sophus Lie: Normal forms of two-dimensional metrics admitting two projective vector fields. Mathematische Annalen, 340(2), 437–463. https://doi.org/10.1007/s00208-007-0158-3
Bryant, R. L., G. Manno, and V. S. Matveev. “A solution of a problem of Sophus Lie: Normal forms of two-dimensional metrics admitting two projective vector fields.” Mathematische Annalen 340, no. 2 (2008): 437–63. https://doi.org/10.1007/s00208-007-0158-3.
Bryant RL, Manno G, Matveev VS. A solution of a problem of Sophus Lie: Normal forms of two-dimensional metrics admitting two projective vector fields. Mathematische Annalen. 2008;340(2):437–63.
Bryant, R. L., et al. “A solution of a problem of Sophus Lie: Normal forms of two-dimensional metrics admitting two projective vector fields.” Mathematische Annalen, vol. 340, no. 2, 2008, pp. 437–63. Scival, doi:10.1007/s00208-007-0158-3.
Bryant RL, Manno G, Matveev VS. A solution of a problem of Sophus Lie: Normal forms of two-dimensional metrics admitting two projective vector fields. Mathematische Annalen. 2008;340(2):437–463.
Journal cover image

Published In

Mathematische Annalen

DOI

ISSN

0025-5831

Publication Date

2008

Volume

340

Issue

2

Start / End Page

437 / 463

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics