Abstract
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 [1].
Similar content being viewed by others
References
Kuz’minov V. I. and Shvedov I. A., “On compact solvability of the operator of exterior derivation,” Siberian Math. J., 38, No. 3, 492–506 (1997).
Federer H., Geometric Measure Theory, Springer-Verlag, Berlin (1996).
Gaffney M. P., “A special Stokes’s theorem for complete Riemannian manifolds,” Ann. Math., 60, No. 1, 140–145 (1954).
Gol’dshtein V. M., Kuz’minov V. I., and Shvedov I. A., “A property of de Rham regularization operators,” Siberian Math. J., 25, No. 2, 251–257 (1984).
Kuz’minov V. I. and Shvedov I. A., “Homological aspects of the theory of Banach complexes,” Siberian Math. J., 40, No. 4, 754–763 (1999).
Gol’dshtein V. M., Kuz’minov V. I., and Shvedov I. A., “The L p -cohomology of Riemannian manifolds,” in: Studies in Geometry and Mathematical Analysis [in Russian], Trudy Inst. Mat. Vol. 7 (Novosibirsk), Nauka, Novosibirsk, 1987, pp. 101–116.
Kato T., Perturbation Theory for Linear Operators, Springer-Verlag, Berlin (1995).
Author information
Authors and Affiliations
Additional information
Original Russian Text Copyright © 2007 Kuz’minov V. I. and Shvedov I. A.
__________
Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 3, pp. 621–630, May–June, 2007.
Rights and permissions
About this article
Cite this article
Kuz’minov, V.I., Shvedov, I.A. On the operator of exterior derivation on the Riemannian manifolds with cylindrical ends. Sib Math J 48, 500–507 (2007). https://doi.org/10.1007/s11202-007-0052-y
Received:
Issue Date:
DOI: https://doi.org/10.1007/s11202-007-0052-y