2022-08-10T05:07:22Zhttps://soar-ir.repo.nii.ac.jp/oaioai:soar-ir.repo.nii.ac.jp:000120572022-06-29T02:21:21ZVector Analysis on Sobolev SpacesASADA, Akira(∞-p)-forms on a k-th Sobolev space Wk(X), X a compact (spin) manifold, is defined by using Sobolev duality. Integrals of (∞-p)-forms on a cube in Wk(X) are defined without using measure. It is shown that exterior differentiability of an (∞-p) -form is astrong constraint and an exterior differentiable (∞-p)-form is always globally exact. As a consequence, the exterior differential operator d is not nilpotent when acting on the space of (∞-p)-forms. Stokes' Theorem for the integrals of (∞-p)-forms is also shown.Article信州大学理学部紀要 31(1): 7-20(1996)departmental bulletin paper信州大学理学部1996-11-29application/pdf信州大学理学部紀要1317200583-063XAA00697923https://soar-ir.repo.nii.ac.jp/record/12057/files/Science31-01-02.pdfeng