Isometries homotopic to the identity
HTML articles powered by AMS MathViewer
- by Douglas A. Norris PDF
- Proc. Amer. Math. Soc. 105 (1989), 692-696 Request permission
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 $L \times {R^1}$.References
- Werner Ballmann, Mikhael Gromov, and Viktor Schroeder, Manifolds of nonpositive curvature, Progress in Mathematics, vol. 61, Birkhäuser Boston, Inc., Boston, MA, 1985. MR 823981, DOI 10.1007/978-1-4684-9159-3
- R. L. Bishop and B. O’Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc. 145 (1969), 1–49. MR 251664, DOI 10.1090/S0002-9947-1969-0251664-4
- S. Bochner, Vector fields and Ricci curvature, Bull. Amer. Math. Soc. 52 (1946), 776–797. MR 18022, DOI 10.1090/S0002-9904-1946-08647-4
- Patrick Eberlein, Surfaces of nonpositive curvature, Mem. Amer. Math. Soc. 20 (1979), no. 218, x+90. MR 533654, DOI 10.1090/memo/0218
- P. Eberlein and B. O’Neill, Visibility manifolds, Pacific J. Math. 46 (1973), 45–109. MR 336648
- T. Frankel, On theorems of Hurwitz and Bochner, J. Math. Mech. 15 (1966), 373–377. MR 0192450
- Ernst Heintze and Hans-Christoph Im Hof, Geometry of horospheres, J. Differential Geometry 12 (1977), no. 4, 481–491 (1978). MR 512919
- Shoshichi Kobayashi, Transformation groups in differential geometry, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 70, Springer-Verlag, New York-Heidelberg, 1972. MR 0355886
- George Springer, Introduction to Riemann surfaces, Addison-Wesley Publishing Co., Inc., Reading, Mass., 1957. MR 0092855
- Joseph A. Wolf, Spaces of constant curvature, McGraw-Hill Book Co., New York-London-Sydney, 1967. MR 0217740
Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 105 (1989), 692-696
- MSC: Primary 53C20
- DOI: https://doi.org/10.1090/S0002-9939-1989-0931744-6
- MathSciNet review: 931744