(α,β)-Metrics with killing β of constant length

Document Type : Original Article

Authors

1 Amirkabir university

2 Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic)

Abstract

The class of (α,β)-metrics is a rich and important class of Finsler metrics, which is extensively studied. Here, we study (α,β)-metrics with Killing of constant length 1-form β and find a simplified formula for their Ricci curvatures. Then, we
show that if F=α+β+b\frac{β^2}{α} is an Einstein Finsler metric, then α is an Einstein Riemann metric.

Keywords

Main Subjects

History

• Receive Date: 09 March 2018
• Revise Date: 30 July 2018
• Accept Date: 17 August 2018