Geometric structures in $Sol_3$
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.
- Publication:
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arXiv e-prints
- Pub Date:
- February 2023
- DOI:
- arXiv:
- arXiv:2302.02543
- Bibcode:
- 2023arXiv230202543L
- Keywords:
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- Mathematics - Differential Geometry
- E-Print:
- 35 pages. arXiv admin note: substantial text overlap with arXiv:2212.12243