Geometric structures in $So{l}_3$

Abstract

In this paper, we conclude the geometric structures in $So{l}_3$ with the Levi-Civita connection and the semi-symmetric non-metric connection. We discuss two special cases to study the geometric structures in $So{l}_3$ with the semi-symmetric non-metric connection, namely $\hat{P}=a(X_3){\partial }_3$ and $\hat{P}=b(X_3){\partial }_1$, also get relatively complete conclusions respectively. As a special case, we investigate the geometric structures in $So{l}_3$ with the Levi-Civita connection.

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