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Bounded manifoldのRelative cyclesの上のDifferential formsについて


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Title: Bounded manifoldのRelative cyclesの上のDifferential formsについて
Other Titles: Differential Forms on Relative Cycles of Bounded Manifold
Authors: 宮本, 尭夫
Authors (alternative): Miyamoto, Takao
Issue Date: 28-Feb-1971
Publisher: 長崎大学教育学部
Citation: 長崎大学教育学部自然科学研究報告. vol.22, p.9-30; 1971
Abstract: The relation between differentiable closed manifold and differential forms on the manifold is well known as the Theory of De Rham-Kodaira. As for every differentiable closed manifold, the number of independent differential forms (degree p) and p-th Betti number of the Manifold are equal. This paper investigates the relation between the differentiable manifold with boundary B and differentiable forms on the manifold, by the same methed as in the Theory of De Rham-Kodaira except that the condition "Closed" is removed form the Theory. That is, we take the p-chain whose boundary belongs to boundary B of the given manifold, in stead of representative p-cycle of Homology group of the closed manifold, call it relative cycle (mod B), and consider the periods of differential forms on the relative cycle as an analogue of the periods of differential forms on any cycle of differential closed manifold. By making use of Duality Theorem of Lefschetz to study the relation between the diffentiable manifold with boundary B and the differential forms, we got following results.
URI: http://hdl.handle.net/10069/33038
ISSN: 0386443X
Type: Departmental Bulletin Paper
Text Version: publisher
Appears in Collections:No. 22

Citable URI : http://hdl.handle.net/10069/33038

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