发表机构
Universidade de Brasília（巴西利亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究具有调和Weyl张量和零径向Weyl曲率的多重扭曲积，证明其至多有三纤维，并利用共形变换和相容性方程刻画局部几何，所得度量源于两类构造，且界是精确的。
AI 中文摘要
本文研究具有一维基、调和Weyl张量和零径向Weyl曲率的多重扭曲积。我们证明这些流形至多具有三个纤维，并描述其局部几何。证明使用了共形变换，使扭曲函数成为二次多项式，并结合Ricci张量施加的相容性方程。所得度量要么由局部共形平坦的多重扭曲积通过将其空间形式纤维替换为Einstein流形而获得，要么属于具有相等纤维维数和正Einstein常数的三纤维族。例子表明该界是精确的，且两个Weyl条件互不蕴含。我们还讨论了由孤子型方程产生的更强限制。
英文摘要
In this article, we study multiply warped products with a one-dimensional base, harmonic Weyl tensor and zero radial Weyl curvature. We prove that these manifolds have at most three fibers and describe their local geometry. The proof uses a conformal change which makes the warping functions quadratic polynomials, together with the compatibility equations imposed by the Ricci tensor. The resulting metrics are either obtained from locally conformally flat multiply warped products by replacing their space-form fibers with Einstein manifolds, or belong to a three-fiber family with equal fiber dimensions and positive Einstein constants. Examples show that the bound is sharp and that neither Weyl condition implies the other. We also discuss the stronger restrictions arising from soliton-type equations.
Comments14 pages
