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On the operator of exterior derivation on the Riemannian manifolds with cylindrical ends. (Russian, English) Zbl 1164.58305
Sib. Mat. Zh. 48, No. 3, 621-630 (2007); translation in Sib. Math. J. 48, No. 3, 500-507 (2007).
Summary: We formulate some conditions for the normal and compact solvability of the operator of exterior derivation on the cylindrical manifolds equipped with some Riemannian metrics. Some analogous results were obtained in the particular case of warped cylinders in the authors’ paper [Sib. Math. J. 38, No. 3, 492–506 (1997; Zbl 0870.58003)].

MSC:
58A10 Differential forms in global analysis
53C20 Global Riemannian geometry, including pinching
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
53C65 Integral geometry
Citations:
Zbl 0870.58003
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