Invariant Einstein Kropina metrics on Lie groups and homogeneous spaces

Masoumeh Hosseini, Hamid Reza Salimi Moghaddam

Published 2018-07-27Version 1

In this article, we study Einstein Kropina metrics on Lie groups and homogeneous spaces. We give a simple way to build the Einstein Kropina metrics on Lie groups. As an example of this method, we construct a family of non-Riemannian Einstein Kropina metrics on the special orthogonal group $SO(n)$. Then we classify all left invariant Einstein Kropina metrics on simply connected $3$-dimensional real Lie groups. Finally, we provide a way for constructing Einstein Kropina metrics on homogeneous spaces. Using this way, we study invariant Einstein Kropina metrics on $S^n$ and show that any projective space admits a non-Riemannian invariant Einstein Kropina metric.