TY - JOUR
ID - 3038
TI - $(\alpha,\beta)$-Metrics with killing $\beta$ of constant length
JO - AUT Journal of Mathematics and Computing
JA - AJMC
LA - en
SN - 2783-2449
AU - Tabatabaeifar, Tayebeh
AU - Najafi, Behzad
AD - Department of Mathematics and Computer Science, Amirkabir University of Technology, 424, Hafez Ave., Tehran 15914, Iran
Y1 - 2020
PY - 2020
VL - 1
IS - 1
SP - 27
EP - 36
KW - Finsler metric
KW - $(\alpha,\beta)$-metric
KW - Einstein manifold
DO - 10.22060/ajmc.2018.3038
N2 - The class of $(\alpha,\beta)$-metrics is a rich and important class of Finsler metrics, which is extensively studied. Here, we study $(\alpha,\beta)$-metrics with Killing of constant length $1$-form $\beta$ and find a simplified formula for their Ricci curvatures. Then, we show that if $F=\alpha+\alpha\beta+b\frac{{\beta}^2}{\alpha}$ is an Einstein Finsler metric, then $\alpha$ is an Einstein Riemann metric.
UR - https://ajmc.aut.ac.ir/article_3038.html
L1 - https://ajmc.aut.ac.ir/article_3038_ec3b89402c7338eacb774d68fb1a1cb0.pdf
ER -