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Isometries homotopic to the identity

Author: Douglas A. Norris
Journal: Proc. Amer. Math. Soc. 105 (1989), 692-696
MSC: Primary 53C20
MathSciNet review: 931744
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Abstract: The types of surfaces which admit nontrivial isometries homotopic to the identity are classified up to diffeomorphism. In dimension three this is done for complete manifolds of constant negative curvature. Three-dimensional visibility manifolds that admit nontrivial isometries homotopic to the identity are shown to be diffeomorphic to a product $ L \times {R^1}$.

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  • [1] Werner Ballman, Mikhael Gromov and Viktor Schroeder, Manifolds of nonpositive curvature, Birkhäuser, Boston, 1985. MR 823981 (87h:53050)
  • [2] R. Bishop and B. O'Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc. 145 (1969), 1-49. MR 0251664 (40:4891)
  • [3] S. Bochner, Vector fields and Ricci curvature, Bull. Amer. Math. Soc. 52 (1946), 776-797. MR 0018022 (8:230a)
  • [4] P. Eberlein, Surfaces of nonpositive curvature, Mem. Amer. Math. Soc. No. 218 (1979). MR 533654 (80j:53044)
  • [5] P. Eberlein and B. O'Neill, Visibility manifolds, Pacific J. Math. 46 (1973), 45-110. MR 0336648 (49:1421)
  • [6] T. Frankel, On theorems of Hurwitz and Bochner, J. Math. Mech. 15 (1966), 373-377. MR 0192450 (33:675)
  • [7] E. Heintze and H. C. Im Hof, Geometry of horospheres, J. Differential Geom. 12 (1977), 481-491. MR 512919 (80a:53051)
  • [8] S. Kobayashi, Transformation groups in differential geometry, Springer-Verlag, New York, 1972. MR 0355886 (50:8360)
  • [9] G. Springer, Introduction to Riemann surfaces, Addison-Wesley, Reading, Massachusetts, 1957. MR 0092855 (19:1169g)
  • [10] J. A. Wolf, Spaces of constant curvature, McGraw-Hill, New York, 1967. MR 0217740 (36:829)

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