  We introduce the notion of a generalized metric n-Leibniz algebra and show
that there is a one-to-one correspondence between generalized metric n-Leibniz
algebras and faithful generalized orthogonal representations of metric Lie
algebras (called Lie triple data). We further show that there is also a
one-to-one correspondence between generalized orthogonal derivations (resp.
generalized orthogonal automorphisms) on generalized metric n-Leibniz algebras
and Lie triple datas.
