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Warped products of metric spaces of curvature
bounded from above
Author:
Chien-Hsiung Chen
Journal:
Trans. Amer. Math. Soc. 351 (1999), 4727-4740
MSC (1991):
Primary 53C20, 53C21, 53C45
Posted:
August 27, 1999
MathSciNet review:
1466944
Full-text PDF Free Access
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Additional Information
Abstract: In this work we extend the idea of warped products, which was previously defined on smooth Riemannian manifolds, to geodesic metric spaces and prove the analogue of the theorems on spaces with curvature bounded from above.
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- S. B. Alexander, I. D. Berg, and R. L. Bishop, Geometric curvature bounds in Riemannian manifolds with boundary, Trans. Amer. Math. Soc. 339 (1993), 703-716. MR 93m:53034
- [2]
- S. B. Alexander and R. L. Bishop, The Hadamard-Cartan theorem in locally convex spaces, Enseign. Math. 36 (1990), 309-320. MR 92c:53044
- [3]
- A. D. Alexandrov, A theorem on triangles in a metric space and some of its applications, Trudy Mat. Inst. Steklov. 38 (1951), 5-23. MR 14:198a
- [4]
- A. D. Alexandrov, Über eine Verallgemeinerung der Riemannschen Geometrie, Schr. Forschungsinst. Math. 1 (1957), 33-84. MR 19:304h
- [5]
- A. D. Alexandrov, V. N. Berestovskii, and I. G. Nikolaev, Generalized Riemannian spaces, Russian Math. Surveys 41 (1986), 1-54. MR 88e:53103
- [6]
- V. N. Berestovskii and I. G. Nikolaev, Multidimensional generalized Riemannian spaces, In book: Encyclopaedia of Math. Sciences 70, Springer, 1993, 184-242. CMP 94:08
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- R. L. Bishop and B. O'Neill, Manifolds of negative curvature, Tran. Amer. Math. Soc. 145 (1969), 1-49. MR 40:4891
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- M. Bridson and A. Haefliger, Metric Spaces of Non-positive Curvature (to appear).
- [9]
- Yu. D. Burago, M. Gromov, and G. Perelman, A. D. Aleksandrov spaces with curvatures bounded below, Russian Math. Surveys 47:2 (1992), 1-58.
- [10]
- H. Busemann, Spaces with non-positive curvature, Acta Mathematica 80 (1948), 259-310. MR 10:623g
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- S. Buyalo, Lecture notes on spaces of nonpositive curvature, course taught at UIUC Spring (1995).
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- C. H. Chen, Warped products of metric spaces of curvature bounded from above, Trans. Amer. Math. Soc. (to appear). CMP 97:17
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 -adic superrigidity for lattices in groups of rank one, IHES Publications Math. 76 (1992). MR 94e:58032
- [16]
- I. G. Nikolaev, Spaces of bounded curvature, lecture notes (1995), Urbana, Illinois.
- [17]
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- [18]
- B. O'Neill, Semi-Riemannian geometry with applications to relativity, Academic Press, New York, 1983. MR 85f:53002
- [19]
- Yu. G. Reshetnyak, On the theory of spaces of curvature not greater than , Mat. Sb. 52 (1960), 789-798.
- [20]
- Yu. G. Reshetnyak, Personal communication.
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Additional Information
Chien-Hsiung Chen
Affiliation:
Department of Mathematics, National Changhua University of Education, Paisa Village, Changhua 50058, Taiwan, R.O.C.
Email:
chen@math.ncue.edu.tw
DOI:
http://dx.doi.org/10.1090/S0002-9947-99-02154-6
PII:
S 0002-9947(99)02154-6
Received by editor(s):
January 29, 1997
Posted:
August 27, 1999
Article copyright:
© Copyright 1999 American Mathematical Society
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