Communications of the
Korean Mathematical Society CKMS

In a Finsler space, we introduce a special $(\alpha ,\beta )$-metric $L$ satisfying $L^{2}(\alpha ,\beta ) = c_{1}\alpha ^{2} + 2c_{2}\alpha \beta + c_{3}\beta ^{2},$ where $c_{i}$ are constants. We investigate the Berwald connection in a Finsler space with this special $(\alpha ,\beta )$-metric.

Keywords: $(\alpha ,\beta )$-metric, Randers metric, Berwald connection, general Kropina metric, Berwald space

MSC numbers: 53B40