Skip to main content
Log in

On the operator of exterior derivation on the Riemannian manifolds with cylindrical ends

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

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].

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. 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).

    MATH  MathSciNet  Google Scholar 

  2. Federer H., Geometric Measure Theory, Springer-Verlag, Berlin (1996).

    MATH  Google Scholar 

  3. Gaffney M. P., “A special Stokes’s theorem for complete Riemannian manifolds,” Ann. Math., 60, No. 1, 140–145 (1954).

    Article  MathSciNet  Google Scholar 

  4. 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).

    Article  MathSciNet  Google Scholar 

  5. 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).

    MathSciNet  Google Scholar 

  6. 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.

    Google Scholar 

  7. Kato T., Perturbation Theory for Linear Operators, Springer-Verlag, Berlin (1995).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

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

Reprints 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

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11202-007-0052-y

Keywords

Navigation