Geometrizing infinite dimensional locally compact groups

Transactions of the American Mathematical Society

Volumn 348, Issue 3, 1996, Pages 941-962

  Plaut, Conrad ^a  

^a UNIVERSITY OF TENNESSEE   (United States)

Author keywords

Alexandrov curvature; Invariant metric; Locally compact groups

Indexed keywords

EID: 21344432304     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-96-01592-9     Document Type: Article

References (25)

1. Alexandrov, A.D., Die innere Geometrie der konvexen Flächen, Akad. Verl., Berlin, 1955. MR 17:74
2. Alexandrov, A.D., Berestovskii, V.N., and Nikolaev, I.G., Generalized Riemannian spaces, Russian Math Surveys 41 (1986) 1-54. MR 88e:53103
3. Berestovskii, V. N., Spaces with bounded curvature and distance geometry, Siberian Math. J. 27 (1986) 8-19. MR 89k:53063
4. Berestovskii, V. N., Homogeneous spaces with intrinsic metric, Soviet Math. Dokl. 27 (1989) 60-63.
5. Berestovskii, V. N., and Plaut, C., Homogeneous spaces of curvature bounded below, preprint.
6. Cheeger, J., and Ebin, D., Comparison theorems in Riemannian geometry, North-Holland Math Library 9 (1975), Amsterdam. MR 56:16538
7. Burago, Yu., Gromov, M., and Perelman, G., A.D. Alexandrov spaces with curvature bounded below, Russian Math Surveys 47 (1992) 1-58. MR 93m:53035
8. Cohn-Vossen, S., Existenz kürzester Wege, Dokl. Math. SSSR 8 (1935) 339-342.
9. Gluskov, V.N., The structure of locally compact groups and Hubert's Fifth Problem, AMS Translations 15 (1960) 55-94. MR 22:5690
10. Gromov, M., Lafontaine, J., and Pansu, P., Structures métrique pours les variétés riemanniannes, Textes Math., vol. 1 CEDIC/Fernand Nathan, 1981. MR 85e:53051
11. Grove, K., Metric differential geometry, Differential Geometry, Lecture Notes in Math., vol. 1263, Springer (1987) 171-227. MR 88i:53075
12. Helgason, S., Differential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, New York, 1978. MR 80k:53081
13. Hurewicz, W. and Wallman, H., Dimension Theory, Princeton U. Press, Princeton, 1941. MR3:312b
14. Lashof, R., Lie algebras of locally compact groups, Pac. J. Math. 7 (1957) 1145-1162. MR 19:1064a
15. Montgomery, D. and Zippin, L., Topological transformation groups, Interscience, New York, 1955. MR 17:383b
16. O'Neill, B., The fundamental equations of a sumersion, Michigan Math J. 13 (1966), 459-469. MR 34:751
17. Plaut, C., Almost Riemannian spaces, J. Diff. Geom. 34 (1991) 515-537. MR 92h:53047
18. Plaut, C., Metric curvature, convergence, and topological finiteness, Duke Math. J. 66 (1992) 43-57. MR 93e:53051
19. Plaut, C., Metric pinching of locally symmetric spaces, Duke Math. J. 73 (1994) 155-162. MR 95c:53055
20. Plaut, C., Correction to "Metric pinching of locally symmetric spaces", Duke Math. J., 75 (1994) 527-528. CMP 94:17
21. Plaut, C., Spaces of Wald curvature bounded below, J. Geom. Analysis, to appear.
22. Rickert, N. W., Arcs in Locally Compact Groups, Math. Annalen 172 (1967), 222-228. MR 35:4331
23. Rickert, N., Some Properties of Locally Compact Groups, J. Austral. Math. Soc. 7 (1967) 433-454. MR 36:2735
24. Rinow, W., Die Innere Geometrie der Metrischen Räume, Springer, Berlin, 1961. MR 23:A1290
25. van Kampen, E. R., The structure of a compact connected group, Amer. J. Math. 57 (1935) 301-308.