On the Volume of a Domain Obtained by a Holomorphic Motion Along a Complex Curve

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• 作者：M.Carmen Domingo-Juan and Vicente Miquel
• 关键词：Pappus formulae ; tube ; volume ; complex space form ; holomorphic motion along a complex submanifold
• 刊名：Annals of Global Analysis and Geometry
• 出版年：2004
• 出版时间：2004
• 年：2004
• 卷：26
• 期：3
• 页码：253-269
• 全文大小：140 KB

文摘

Let D be a domain obtained by a holomorphic motion of a domain D_p M_pn–1 along a complex curve P in a complex space form Mn. We prove that, if n= 2, the volume of D depends only on the geometry of D_p and the intrinsic geometry of P, but not on the extrinsic geometry of P. When M is closed (compact without boundary), then the dependence on P is only through its topology. When n > 2, and for arbitrary domains D_p, a similar result holds only for Frenet motions, but when D_p has certain integral symmetries (and only in this case) this result is still true for any motion .