标题： 弯曲的Witten-Dijkgraaf-Verlinde-Verlinde方程与${\cal N}{=}\,4$力学 显示英文标题

标题： Curved Witten-Dijkgraaf-Verlinde-Verlinde equation and ${\cal N}{=}\,4$ mechanics

摘要： 我们提出了一种广义的Witten-Dijkgraaf-Verlinde-Verlinde（WDVV）方程，从${\mathbb R}^n$推广到任意黎曼流形。 其形式通过将WDVV方程与${\cal N}{=}\,4$超对称$n$维力学之间的关系从平坦空间扩展到弯曲空间而获得。 所得的“弯曲WDVV方程”由三阶Codazzi张量表示。 对于满足简单约束条件的平坦空间WDVV解，我们以度规的旋转不变共形因子的形式，为任意各向同性空间提供了一个弯曲空间解。 显示英文摘要

摘要： We propose a generalization of the Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equation from ${\mathbb R}^n$ to an arbitrary Riemannian manifold. Its form is obtained by extending the relation of the WDVV equation with ${\cal N}{=}\,4$ supersymmetric $n$-dimensional mechanics from flat to curved space. The resulting `curved WDVV equation' is written in terms of a third-rank Codazzi tensor. For every flat-space WDVV solution subject to a simple constraint we provide a curved-space solution on any isotropic space, in terms of the rotationally invariant conformal factor of the metric.