On Randers manifolds with semi-symmetric compatible linear connections
The paper deals with metric semi-symmetric linear connections of Randers manifolds \(\mathcal R^n\). These manifolds are special Finsler manifolds with Finsler metric \(F(v)=\sqrt{\alpha(v,v)}+\beta(v)\), where \(\alpha\) is a Riemann metric, and \(\beta\) is a 1-form (addition of \(\beta(v)\) means a linear perturbation of the Riemann metric). After showing that \(\mathcal R^n\) is a generalized Berwald manifold if and only if \(\nabla \alpha=\nabla\beta=0\), where \(\nabla\) is a linear metric connection of \(\mathcal R^n\), and iff the Riemann norm of \(\beta^\sharp\) is constant, in the main theorem the author proves 8 properties of \(\beta\), provided that \(\mathcal R^n\) has a metric semi-symmetric linear connection. In the last part of the paper those Riemann manifolds are characterized, which admit 1-form perturbations, such that the resulting \(\mathcal R^n\) has a metric semi-symmetric connection. Also several examples are given.
scientific article; zbMATH DE number 6418459
scientific article