Geometry of conformal vector fields

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• 作者：Sharief Deshmukh ^{shariefd@ksu.edu.sa}
• 关键词：Conformal vector fields ; Ricci curvature ; Scalar curvature ; Obata&rsquo ; s theorem ; Laplacian ; φφ-analytic vector fields
• 刊名：Arab Journal of Mathematical Sciences
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：23
• 期：1
• 页码：44-73
• 全文大小：372 K
• 卷排序：23

文摘

It is well known that the Euclidean space (Rn,〈,〉)(Rn,〈,〉), the nn-sphere Sn(c)Sn(c) of constant curvature cc and Euclidean complex space form (Cn,J,〈,〉)(Cn,J,〈,〉) are examples of spaces admitting conformal vector fields and therefore conformal vector fields are used in obtaining characterizations of these spaces. In this article, we study the conformal vector fields on a Riemannian manifold and present the existing results as well as some new results on the characterization of these spaces. Taking clue from the analytic vector fields on a complex manifold, we define φφ-analytic conformal vector fields on a Riemannian manifold and study their properties as well as obtain characterizations of the Euclidean space (Rn,〈,〉)(Rn,〈,〉) and the nn-sphere Sn(c)Sn(c) of constant curvature cc using these vector fields.