(untitled) (Communications in Mathematical Research, 2021)
In this article, we study the Lie supertriple system (LSTS) T over a field K admitting a nondegenerate invariant supersymmetric bilinear form (call such a T metrisable). We give the definition of T^∗_ω-extension of an LSTS T, prove a necessary and sufficient condition for a metrised LSTS (T, ϕ) to be isometric to a T^∗-extension of some LSTS, and determine when two T^∗-extensions of an LSTS are "same", i.e., they are equivalent or isometrically equivalent.