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PreprintCC BY 4.0arXiv

Classification of analytic SOo(p,q)-actions on closed (p+q−1)-dimensional manifolds II : p ≥ 3, q=1,2

  • Spyridon Lentas
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Abstract

This paper provides a classification of analytic actions of the semi-orthogonal groups SO∘(p,1) and SO∘(p,2), for p ≥ 3, on closed, connected manifolds of dimension p and p+1 respectively. It is a sequel to a previous paper, which treats the case p,q ≥ 3. Adapting Uchida's methods, we explicitly construct analytic actions of SO∘(p,1) on Sp and Sp−1 × S1, and analytic actions of SO∘(p,2) on Sp+1, Sp × S1 and Sp−1 × S2, and we classify them up to analytic isomorphism, using a result of Hitchin and Schneider's classification of analytic SL2(ℝ) actions on surfaces. The main result demonstrates that any analytic SO∘(p,q) action, q=1,2, on a closed, connected (p+q−1)-dimensional manifold is covered by one of the constructed actions or by an action on SO∘(p,q) ×P S1, where P is a maximal parabolic subgroup of SO∘(p,q).

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Cite

BibTeXRIS
BibTeX
@misc{lentas2026classification,
  title = {{Classification of analytic $\textSO^o(p,q)$-actions on closed $(p+q-1)$-dimensional manifolds II : $p \geq 3$, $q=1,2$}},
  author = {Spyridon Lentas},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.08149},
  eprint = {2611.08149},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.08149},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Classification of analytic SO^o(p,q)-actions on closed (p+q−1)-dimensional manifolds II : p ≥ 3, q=1,2
AU  - Spyridon Lentas
PY  - 2026
DA  - 2026/11/05
PB  - arXiv
DO  - 10.48550/arxiv.2611.08149
UR  - https://arxiv.org/abs/2611.08149
AB  - This paper provides a classification of analytic actions of the semi-orthogonal groups SO^∘(p,1) and SO^∘(p,2), for p ≥ 3, on closed, connected manifolds of dimension p and p+1 respectively. It is a sequel to a previous paper, which treats the case p,q ≥ 3. Adapting Uchida's methods, we explicitly construct analytic actions of SO^∘(p,1) on S^p and S^p−1 × S^1, and analytic actions of SO^∘(p,2) on S^p+1, S^p × S^1 and S^p−1 × S^2, and we classify them up to analytic isomorphism, using a result of Hitchin and Schneider's classification of analytic SL_2(ℝ) actions on surfaces. The main result demonstrates that any analytic SO^∘(p,q) action, q=1,2, on a closed, connected (p+q−1)-dimensional manifold is covered by one of the constructed actions or by an action on SO^∘(p,q) ×_P S^1, where P is a maximal parabolic subgroup of SO^∘(p,q).
ER  -