M. Bordemann has studied non-associative algebras with nondegenerate associative bilinear forms. In this paper, we focus on pseudo-Riemannian bilinear forms and study pseudo-Riemannian Leibniz algebras, i.e., Leibniz algebras with pseudo-Riemannian non-degenerate symmetric bilinear forms. We give the notion and some properties of T*-extensions of Leibniz algebras. In addition, we introduce the definition of equivalence and isometrical equivalence for two T*-extensions of a Leibniz algebra, and give a sufficient and necessary condition for the equivalence and isometrical equivalence.
In this paper, we consider the stochastic Korteweg-de Vries-Benjamin-Ono equation with white noise. Using Fourier restriction norm method and some basic inequalities, we obtain a local existence and uniqueness result for the solution of this problem. We also get global existence of the L2(ℝ) solution.