Topics in differential geometry associated with position vector fields on Euclidean submanifolds

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• 作者：Bang-Yen Chen ^{bychen@math.msu.edu}
• 关键词：Position vector field ; Rectifying curve ; Rectifying submanifold ; Finite type submanifold ; Ricci soliton ; Biharmonic submanifold ; Constant-ratio submanifold ; Self-shrinker ; Thompson&rsquo ; s law of natural growth
• 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：1-17
• 全文大小：332 K
• 卷排序：23

文摘

The position vector field is the most elementary and natural geometric object on a Euclidean submanifold. The purpose of this article is to survey six research topics in differential geometry in which the position vector field plays very important roles. In this article we also explain the relationship between position vector fields and mechanics, dynamics, and D’Arcy Thompson’s law of natural growth in biology.