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arXiv · 2405.12831

Constant sectional curvature surfaces with a semi-symmetric non-metric connection

Muhittin Evren Aydin·Rafael López·Adela Mihai
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Abstract

Consider the Euclidean space $\mathbb{R}^3$ endowed with a canonical semi-symmetric non-metric connection determined by a vector field $\mathsf{C}\in\mathfrak{X}(\mathbb{R}^3)$. We study surfaces when the sectional curvature with respect to this connection is constant. In case that the surface is cylindrical, we obtain full classification when the rulings are orthogonal or parallel to $\mathsf{C}$. If the surface is rotational, we prove that the rotation axis is parallel to $\mathsf{C}$ and we classify all conical rotational surfaces with constant sectional curvature. Finally, for the particular case $\frac12$ of the sectional curvature, the existence of rotational surfaces orthogonally intersecting the rotation axis is also obtained.

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Muhittin Evren Aydin, Rafael López, Adela Mihai. 2024-05-21. Constant sectional curvature surfaces with a semi-symmetric non-metric connection. https://arxiv.org/abs/2405.12831

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