manuscripta mathematica

, Volume 96, Issue 4, pp 487–505

Warped products of Hadamard spaces

  • Stephanie B. Alexander
  • Richard L. Bishop

DOI: 10.1007/s002290050078

Cite this article as:
Alexander, S. & Bishop, R. manuscripta math. (1998) 96: 487. doi:10.1007/s002290050078


In the Riemannian case, our approach to warped products illuminates curvature formulas that previously seemed formal and somewhat mysterious. Moreover, the geometric approach allows us to study warped products in a much more general class of spaces. For complete metric spaces, it is known that nonpositive curvature in the Alexandrov sense is preserved by gluing on isometric closed convex subsets and by Gromov–Hausdorff limits with strictly positive convexity radius; we show it is also preserved by warped products with convex warping functions.

Mathematics Subject Classification (1991):53C70, 53B20, 53C20 

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Stephanie B. Alexander
    • 1
  • Richard L. Bishop
    • 1
  1. 1.Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green, Urbana, IL 61801, USA.¶e-mail:; bishop@math.uiuc.eduUS

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