Minimal translation surfaces with respect to semi-symmetric connections in $\mathbb{R}^3$ and $\mathbb{R}^3_1$

TL;DR

This paper classifies minimal translation surfaces in Euclidean and Lorentzian 3-space considering semi-symmetric connections, expanding understanding of geometric structures under these specialized connections.

Contribution

It introduces and classifies minimal translation surfaces with respect to semi-symmetric connections in both Euclidean and Lorentzian 3-space.

Findings

Classification of minimal translation surfaces under semi-symmetric metric connections

Classification under semi-symmetric non-metric connections

Extension to both Euclidean and Lorentzian geometries

Abstract

In this paper, we define and classify minimal translation surfaces with respect to a kind of semi-symmetric metric connections and a kind of semi-symmetric non-metric connections in $\mathbb{R}^3$ and $\mathbb{R}^3_1$.