Hostname: page-component-848d4c4894-8bljj Total loading time: 0 Render date: 2024-06-19T11:23:53.486Z Has data issue: false hasContentIssue false
  • English
  • Français

On a construction of complete simply-connected riemannian manifolds with negative curvature

Published online by Cambridge University Press:  22 January 2016

Haruo Kitahara ,
Hajime Kawakami  and
Jin Suk Pak
Haruo Kitahara
Affiliation:
Department of Mathematics Kanazawa University, Kanazawa, 920, Japan
Hajime Kawakami
Affiliation:
Department of Mathematics Kanazawa University, Kanazawa, 920, Japan
Jin Suk Pak
Affiliation:
Department of Mathematics Kyungpook National University, Taegu, 635, Korea
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let M be a complete simply-connected riemannian manifold of even dimension m. J. Dodziuk and I.M. Singer ([D1]) have conjectured that H2p(M) = 0 if p ≠ m/2 and dim H2m/2(M) = ∞, where H2*(M) is the space of L2-harmonic forms on M.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 113 , March 1989 , pp. 7 - 13
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1989

References

[A] Atiyah, M. F., Elliptic operators, discrete groups and von Neumann algebras, Astérisque, 32–33 (1976), 43–72.Google Scholar
[An] Anderson, M. T., L2 -harmonic forms and a conjecture of Dodziuk-Singer, Bull. Amer. Math. Soc., 13 (1985), 163–165.Google Scholar
[B] Besse, A. L., Einstein manifolds, Ergeb. Math. Grenzgeb. 3. folge. Band 10, 1987, Springer-Verlag.Google Scholar
[B-O] O’Neill, R. L. Bishop-B., Manifolds of negative curvature, Trans. Amer. Math. Soc., 145 (1969), 1–49.Google Scholar
[D1] Dodziuk, J., L2-harmonic forms on rotationally symmetric Riemannian manifolds, Proc. of Amer. Math. Soc., 77 (1979), 395–400.Google Scholar
[D2] Dodzuik, J., A private letter.Google Scholar
[K-W] Kazdan, J. L.–Warner, F. W., Curvature functions for open 2-manifolds, Ann. of Math., 99 (1974), 203–219.Google Scholar
[M] Mori, H., Remarks on the Riemannian metric on the double of a manifold with boundary, preprint.Google Scholar
[O-N] Ochiai, T.–Noguchi, J., Geometric Function Theory (in Japanese), Iwanami, 1986.Google Scholar