Submanifold geometry in symmetric spaces

Journal of Differential Geometry

Volumn 42, Issue 3, 1995, Pages 665-718

  Terng, C L ^a,b   Thorbergsson, G ^a,b  

^a NORTHEASTERN UNIVERSITY   (United States)

^b UNIVERSITY OF COLOGNE   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0029679794     PISSN: 0022040X     EISSN: 1945743X     Source Type: Journal    
DOI: 10.4310/jdg/1214457552     Document Type: Article

References (42)

1. A. V. Alekseevsky & D. V. Alekseevsky, Riemannian G-manifold with one-dimensional orbit space, Preprint.
2. R. Bott & H. Samelson, Applications of the theory of Morse to symmetric spaces, Amer. J. Math. 80 (1958) 964-1029.
3. J. Berndt & L. Vanhecke, Curvature adapted submanifolds, Nihonkai Math. J. 3 (1992) 177-185.
4. E. Cartan, Families de surfaces isoparamétriques dans les espaces à courbure constante, Ann. Pura Mat. Appl. (4) 17 (1938) 177-191.
5. S. Carter & A. West, Isoparametric systems and transnormality, Proc. London Math. Soc. 51 (1985) 520-542.
6. S. Carter & A. West, Isoparametric and totally focal submanifolds, Proc. London Math. Soc. 60 (1990) 609-624.
7. T. E. Cecil & S. S. Chern, Tautness and Lie sphere geoemtry, Math. Ann. 278 (1987) 381-399.
8. T. E. Cecil & P. J. Ryan, Tight and taut immersions of manifolds, Res. Notes Math. Vol. 107, Pitman, Boston 1985.
9. L. Conlon, Variational Completeness and K-transversal Domains. J. Differential Geometry 5 (1971) 135-147.
10. L. Conlon, The topology of certain spaces of paths on a compact symmetric space, Trans. Amer. Math. Soc. 112 (1964) 228-248.
11. L. Conlon, Remarks on commuting involutions, Bull. Amer. Math. Soc. 22 (1969) 255-257.
12. J. Dadok Polar coordinates induced by actions of compact Lie groups, Trans. Amer. Math. Soc. 288 (1985) 125-137.
13. D. Ferus, H. Karcher & H. -F. Münzner, Cliffordalgebren und neue isoparametrische Hyperflächen, Math. Z. 177 (1981) 479-502.
14. E. C. Harle, Isoparametric families of submanifolds, Bol. Soc. Brasil Mat. 13 (1982) 35-48.
15. E. Heintze, C. Olmos, &; G. Thorbergsson, Submanifolds with constant principal curvatures and normal holonomy groups, Internat. J. Math. 2 (1991) 167-175.
16. E. Heintze, R. S. Palais, C. L. Terng & G. Thorbergsson, Hyperpolar Actions and k-flat Homogeneous Spaces, J. Reine Angew. Math. 454 (1994) 163-179.
17. E. Heintze, R. S. Palais, C. L. Terng & G. Thorbergsson, Hyperpolar Actions on Symmetric Spaces, Preprint.
18. R. Hermann, Variational completeness for compact symmetric spaces, Proc. Amer. Math. Soc. 11 (1960) 544-546.
19. R. Hermann, Totally geodesic orbits of groups of isometries, Proc. Kon. Nederl. Akad. Wetensch. 65 (1962) 291-298.
20. R. Hermann, On the existence of a fundamental domain for Riemannian transformation groups, Proc. Amer. Math. Soc. 13 (1962) 489-494.
21. V. G. Kac, Infinite dimensional Lie algebras, Third Ed., Cambridge University Press, Cambridge, 1990.
22. O. Loos, Symmetric Spaces, I, II Benjamin, New York, 1969.
23. J. W. Milnor, Morse Theory, Annals of Math. Studies, Vol. 51, Princeton University Press, Princeton, 1963.
24. H. F. Miinzner, Isoparametrische Hyperflächen in Sphären, I, II, Math. Ann. 251 (1980) 57-71; 256 (1981), 215-232.
25. T. Ozawa, On critical sets of distance functions to a taut submanifold, Math. Ann. 276 (1986) 91-96.
26. R. S. Palais, Morse theory on Hilbert manifolds, Topology 2 (1963) 299-340.
27. R. S. Palais & C. L. Terng, A general theory of canonical forms, Trans. Amer. Math. Soc. 300 (1987) 771-789.
28. R. S. Palais & C. L. Terng, Critical Point Theory and Submanifold, Geometry Lecture Notes in Math., Vol. 1353, Springer, Berlin, 1988.
29. U. Pinkall, Dupin hyper surfaces, Math. Ann. 270 (1985) 427-440.
30. U. Pinkall & G. Thorbergsson, Deformations of Dupin hypersurfaces, Proc. Amer. Math. Soc. 107 (1989) 1037-1043.
31. A. Pressley & G. Segal, Loop Groups, Clarendon Press, Oxford, 1986.
32. G. Segal, The representation ring of a compact Lie group, Inst. Hauter Étuder Sci. Publ. Math. 34 (1968) 113-128.
33. C. L. Terng, Isoparametric submanifolds and their Coxeter groups, J. Differential Geometry 21 (1985) 79-107.
34. C. L. Terng, Submanifolds with flat normal bundle, Math. Ann. 277 (1987) 95-111.
35. C. L. Terng, Proper Fredholm submanifolds of Hilbert space, J. Differential Geometry 29 (1989) 9-47.
36. C. L. Terng, Variational completeness and infinite dimensional geometry, Geometry and Topology of Submanifolds, III, World Scientific, Singapore, 1991, 279-293.
37. C. L. Terng, Polar Actions on Hilbert Space, to appear in J. Geom. Anal.
38. G. Thorbergsson, Dupin hypersurfaces, Bull. London Math. Soc. 15 (1983) 493-498.
39. G. Thorbergsson, Isoparametric submanifolds and their buildings, Ann. of Math. 133 (1991) 429-446.
40. Q. -M. Wang, Isoparametric hypersurfaces in complex projective spaces, Proc. 1980 Beijing Sympos. Differential Geometry and Differential Equations, Vol. 3, Science Press, Beijing, 1982, 1509-1524.
41. B. Wu, Hyper-isoparametric submanifolds in Riemannian symmetric spaces, Preprint.
42. B. Wu, Equifocal focal hypersurfaces of rank one symmetric spaces, Preprint.