Homogeneous Einstein metrics on SU(n)

Abstract

It is known that every compact simple Lie group admits a bi-invariant homogeneous Einstein metric. In this paper we use two ansatz to probe the existence of additional inequivalent Einstein metrics on the Lie group SU (n) for arbitrary n. We provide an explicit construction of (2k+1) inequivalent Einstein metrics on SU (2k) and 2k inequivalent Einstein metrics on SU (2k + 1).

10 pages. Research conducted as Graduate Student. Advisor: Dr. Christopher Pope (Dept. of Physics and Astronomy, Texas A&M University)

References in corpus (4)

• Invariant Einstein metrics on flag manifolds with four isotropy summands
• Einstein Metrics on Group Manifolds and Cosets
• Homogeneous Einstein Metrics on SO(n)
• Einstein metrics on compact Lie groups which are not naturally reductive

Cited by in corpus (4)

• Non-naturally reductive Einstein metrics on the compact simple Lie group $F_4$
• New Non-naturally reductive Einstein metrics on Exceptional simple Lie groups
• Non-naturally reductive Einstein metrics on normal homogeneous Einstein manifolds
• New Einstein metrics on the Lie group $SO(n)$ which are not naturally reductive