Warped products of metric spaces of curvature bounded from above
Author:
ChienHsiung Chen
Journal:
Trans. Amer. Math. Soc. 351 (1999), 47274740
MSC (1991):
Primary 53C20, 53C21, 53C45
Published electronically:
August 27, 1999
MathSciNet review:
1466944
Fulltext 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), 703716. MR 93m:53034
 [2]
 S. B. Alexander and R. L. Bishop, The HadamardCartan theorem in locally convex spaces, Enseign. Math. 36 (1990), 309320. 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), 523. MR 14:198a
 [4]
 A. D. Alexandrov, Über eine Verallgemeinerung der Riemannschen Geometrie, Schr. Forschungsinst. Math. 1 (1957), 3384. MR 19:304h
 [5]
 A. D. Alexandrov, V. N. Berestovskii, and I. G. Nikolaev, Generalized Riemannian spaces, Russian Math. Surveys 41 (1986), 154. MR 88e:53103
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 R. L. Bishop and B. O'Neill, Manifolds of negative curvature, Tran. Amer. Math. Soc. 145 (1969), 149. MR 40:4891
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 M. Bridson and A. Haefliger, Metric Spaces of Nonpositive Curvature (to appear).
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 S. Buyalo, Lecture notes on spaces of nonpositive curvature, course taught at UIUC Spring (1995).
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 M. Gromov, Hyperbolic manifolds, groups and actions, Riemann Surfaces and Related Topics (I. Kra and Maskit, eds.), Proceedings, Stony Brook 1978, Annals of Math. Studies, Number 97, Princeton University, 1981, pp. 83213. MR 82m:53035
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 I. G. Nikolaev, Spaces of bounded curvature, lecture notes (1995), Urbana, Illinois.
 [17]
 S. Nölker, Isometric immersions of warped products, Differential Geometry and its Applications 6 (1996), 130. MR 97d:53064
 [18]
 B. O'Neill, SemiRiemannian 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), 789798.
 [20]
 Yu. G. Reshetnyak, Personal communication.
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Additional Information
ChienHsiung 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/S0002994799021546
PII:
S 00029947(99)021546
Received by editor(s):
January 29, 1997
Published electronically:
August 27, 1999
Article copyright:
© Copyright 1999 American Mathematical Society
