Mathematische Zeitschrift

, Volume 227, Issue 3, pp 455–463

Invariant metrics of positive Ricci curvature on principal bundles

  • Peter B. Gilkey
  • JeongHyeong Park
  • Wilderich Tuschmann

Abstract.

Let \(Y\) be a compact connected Riemannian manifold with a metric of positive Ricci curvature. Let \(\pi:P\rightarrow Y\) be a principal bundle over \(Y\) with compact connected structure group \(G\). If the fundamental group of \(P\) is finite, we show that \(P\) admits a \(G\) invariant metric with positive Ricci curvature so that \(\pi\) is a Riemannian submersion.

Mathematics Subject Classification: Mathematics Subject Classification (1991): 53C20. 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Peter B. Gilkey
    • 1
  • JeongHyeong Park
    • 2
  • Wilderich Tuschmann
    • 3
  1. 1. Mathematics Department, University of Oregon, Eugene, OR 97403, USA (e-mail: gilkey@math.uoregon.edu) US
  2. 2. Department of Mathematics, Honam University, Seobongdong 59, Kwangsanku, Kwangju, 506-090, South Korea, (e-mail: jhpark@honam.honam.ac.kr) KR
  3. 3. Max-Planck-Institut für Mathematik, Gottfried-Claren-Strasse 26, D-53225 Bonn, Germany (e-mail: tusch@mis.mpg.de) DE

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