Geometric structures in $Sol_3$

Siyao Liu

Geometric structures in $Sol_3$

Differential Geometry 2023-02-07 v1

Authors: Siyao Liu

Abstract

In this paper, we conclude the geometric structures in $Sol_3$ with the Levi-Civita connection and the semi-symmetric non-metric connection. We discuss two special cases to study the geometric structures in $Sol_3$ with the semi-symmetric non-metric connection, namely $\widehat{P}=a(X_3)\partial_3$ and $\widehat{P}=b(X_3)\partial_1$ , also get relatively complete conclusions respectively. As a special case, we investigate the geometric structures in $Sol_3$ with the Levi-Civita connection.

Cite

@article{arxiv.2302.02543,
  title  = {Geometric structures in $Sol_3$},
  author = {Siyao Liu},
  journal= {arXiv preprint arXiv:2302.02543},
  year   = {2023}
}

Comments

35 pages. arXiv admin note: substantial text overlap with arXiv:2212.12243

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