On the Volume of a Domain Obtained by a Holomorphic Motion Along a Complex Curve |
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Authors: | Domingo-Juan M Carmen Miquel Vicente |
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Institution: | (1) Department of Mathematics, Kyungpook National University, Taegu, 702-701, Korea;(2) Departamento de Geometría y Topología, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain |
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Abstract: | Let D be a domain obtained by a holomorphic motion of a domain D
p M
p
n–1
along a complex curve P in a complex space form M
n
. 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 . |
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Keywords: | Pappus formulae tube volume complex space form holomorphic motion along a complex submanifold |
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