标题： 雅可比-科茨-文伯格结构在雅可比左对称代数上 显示英文标题

标题： Jacobi-Koszul-Vinberg structures on Jacobi-left-symmetric algebroids

摘要： Koszul-Vinberg流形是Hessian流形的推广，它们之间的关系类似于泊松流形和辛流形之间的关系。 Koszul-Vinberg结构和流形上的泊松结构扩展到代数胚上的结构。 左对称代数胚上的Koszul-Vinberg结构被视为李代数胚上泊松结构的对称类似物。 我们在Jacobi-左对称代数胚上定义了一个Jacobi-Koszul-Vinberg结构，作为Jacobi代数胚上Jacobi结构的对称类似物。 我们展示了Jacobi代数胚上Jacobi-Koszul-Vinberg结构的一些性质，并给出了Jacobi-Koszul-Vinberg流形的定义，这是Jacobi流形的对称类似物。 显示英文摘要

摘要： A Koszul-Vinberg manifold is a generalization of a Hessian manifold, and their relation is similar to the relation between Poisson manifolds and symplectic manifolds. Koszul-Vinberg structures and Poisson structures on manifolds extend to the structures on algebroids. A Koszul-Vinberg structure on a left-symmetric algebroid is regarded as a symmetric analogue of a Poisson structure on a Lie algebroid. We define a Jacobi-Koszul-Vinberg structure on a Jacobi-left-symmetric algebroid as a symmetric analogue of a Jacobi structure on a Jacobi algebroid. We show some properties of Jacobi-Koszul-Vinberg structures on Jacobi algebroids and give the definition of a Jacobi-Koszul-Vinberg manifold, which is a symmetric analogue of a Jacobi manifold.