Skip to main content
SpringerLink
Log in

Curvature and homology of Riemannian manifolds with boundary

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Bochner, S.: Vector fields and Ricci curvature. Bull. Amer. Math. Soc.52, 776–797 (1946).

    Google Scholar 

  2. —: Euler-Poincaré characteristic for locally homogeneous and complex spaces. Ann. of Math.51, 241–261 (1950).

    Google Scholar 

  3. Cartan, E.: Leçons sur la géométrie des espaces de Riemann, 2nd ed. Paris 1946.

  4. Conner, P. E.: The Neumann's problem for differential forms on Riemannian manifolds. Mem. Amer. Math. Soc. No. 20 (1956).

  5. Duff, G. F.D., andD. C. Spencer: Harmonic tensors on Riemannian manifolds with boundary. Ann. of Math.56, 128–156 (1952).

    Google Scholar 

  6. Eisenhart, L. P.: Riemannian geometry. Princeton 1949.

  7. Hsiung, C. C.: Curvature and Betti numbers of compact Riemannian manifolds with boundary. Univ. e Politec. Torino. Rend. Sem. Mat.17, 95–131 (1957-58).

    Google Scholar 

  8. —: A note of correction. Univ. e Politec. Torino. Rend. Sem. Mat.21, 127–129 (1961-62).

    Google Scholar 

  9. Lichnerowicz, A.: Courbure, nombre de Betti, et espaces symetriques. Proceedings of the International Congr. of Mathematicians, Cambridge, Mass.2, 216–223 (1950).

    Google Scholar 

  10. Morrey J. R., Morrey C. B.: A variational method in the theory of harmonic integrals. II. Amer. J. Math.78, 137–170 (1956).

    Google Scholar 

  11. Nomizu, K., andH. Ozeki: A theorem on curvature tensor fields. Proc. Nat. Acad. Sci., U.S.A.48, 206–207 (1962).

    Google Scholar 

  12. De Rham, G., andK. Kodaira: Harmonic integrals. Mimeographed notes, Institute for Advanced Study, Princeton 1950.

    Google Scholar 

  13. Yano, K., andS. Bochner: Curvature and Betti numbers. Ann. of Math. Studies, No. 32, Princeton 1953.

Download references

Author information

Authors and Affiliations

  1. Lehigh University, Bethlehem, Pa, (U.S.A.)

    Chuan-Chih Hsiung

Authors
  1. Chuan-Chih Hsiung
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was done at Mathematics Research Center, U. S. Army, Madison, Wisconsin under Contract No. DA-11-022-ORD-2059, and at the University of California, Berkeley, California under National Science Foundation Research Grant NSF G-19137.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hsiung, CC. Curvature and homology of Riemannian manifolds with boundary. Math Z 82, 67–81 (1963). https://doi.org/10.1007/BF01112824

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01112824

Keywords

Search

Navigation