Cohomogeneity one manifolds of even dimension with strictly positive sectional curvature

Journal of Differential Geometry

Volumn 68, Issue 1, 2004, Pages 31-72

  Verdiani, Luigi ^a  

^a Dipartimento di Matematica Applicata G Sansone   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 27744487769     PISSN: 0022040X     EISSN: 1945743X     Source Type: Journal    
DOI: 10.4310/jdg/1102536709     Document Type: Article

References (35)

1. A.V. Alekseevsky & D.V. Alekseevsky, G-manifolds with one dimensional orbit space, Adv. Sov. Math. 8 (1992) 1-31.
2. A.V. Alekseevsky & D.V. Alekseevsky, Riemannian G-manifolds with one dimensional orbit space, Ann. Glob. Anal. Geom. 11 (1993) 197-211.
3. D.V. Alekseevsky & F. Podesta, Compact cohomogeneity one Riemannian manifolds of positive Euler characteristic and quaternionic Kahler manifolds, Proceedings of USA-Brazil Workshop, W. de Gruyter Verlag, Berlin, 1997, 1-33.
4. Y. Bazaikin, On one family of 13-dimensional closed Riemannian manifolds with positive curvature, Siber. Math. J. 37 (1996) 1068-1085.
5. L. Berard-Bergery, Les variétés Riemanniennes homogenes simplement connexes de dimension impaire a courboure strictement positive, J. Math. Pures Appl. 55 (1976) 47-68.
6. H. Borel, Some remarks about Lie groups transitive on spheres and tori, Bull. Amer. Math. Soc. 55 (1949) 580-587.
7. G.E. Bredon, Introduction to compact transformation groups, Academic Press, New York, 1972.
8. M. Buchner, K. Fritzsche & T. Sakai, Geometry and cohomology of certain domains in the complex projective space, J. Reine Angew. Math. 323 (1981) 1-52.
9. J.H. Eschenburg, New examples of manifolds with strictly positive curvature, Invent. Math. 66 (1982) 469-480.
10. J.H. Eschenburg, Inhomogeneous spaces of positive curvature, Diff. Geom. Appl. 2 (1992), 123-132.
11. M. Goto & F.D. Grosshans, Semisimple Lie algebras, M. Dekker, New York-Basel, 1978.
12. K. Grove & C. Searle, Differential topological restrictions curvature and symmetry, J. Differential Geom. 47 (1997) 530-559.
13. K. Grove, K. Shankar & W. Ziller, Cohomogeneity, curvature and fundamental groups, in preparation
14. R. Hamilton, Three-manifolds with positive Ricci curvature, J. Diff. Geom. 17 (1982) 255-306.
15. W.Y. Hsiang & B. Kleiner, On the topology of positively curved 4-manifolds with symmetry, J. Diff. Geom. 30 (1989) 615-621.
16. W.Y. Hsiang & H.B. Lawson, Minimal submanifolds of low cohomogeneity, J. Differential Geom. 5 (1971) 1-38.
17. K. Iwata, Classification of compact transformation groups on cohomology quaternion projective spaces with codimension one orbits, Osaka J. Math. 15 (1978) 475-508.
18. K. Iwata, Compact transformation groups on rational cohomology Cayley projective planes, Tohoku Math. J. 33 (1981) 429-442.
19. P.S. Mostert, On a compact Lie group acting on a manifold, Ann. Math. 65 (1957) 447-455
20. P.S. Mostert, On a compact Lie group acting on a manifold, Ann. Math. 66 (1957) 589.
21. W.G. McKay & J. Patera, Tables of dimensions, indices and branching rules for representations of simple Lie algebras, M. Dekker, New York-Basel, 1981.
22. T. Nagano, Transformation groups with (n - 1) dimensional orbits on non compact manifolds, Nagoya Math. J. 14 (1959) 25-38.
23. A.L. Onishchik & E.B. Vinberg, Lie Groups and Lie Algebras III, Springer Verlag, Berlin, 1994.
24. F. Podesta & L. Verdiani, Totally geodesic orbits of isometries, Ann. Glob. Anal. Geom. 16 (1998) 399-412
25. F. Podesta & L. Verdiani, Totally geodesic orbits of isometries, Ann. Glob. Anal. Geom. 19 (2001) 207-208.
26. F. Podesta & L. Verdiani, Positively curved 7-dimensional manifolds, Quart. Math. Oxford 50 (1999) 497-504.
27. C. Searle, Cohomogeneity and positive curvature in low dimension, Math. Z. 214 (1993) 491-498
28. C. Searle, Cohomogeneity and positive curvature in low dimension, Math. Z. 226 (1997) 165-167.
29. F. Uchida, Classification of compact transformation groups on cohomology complex projective spaces with codimension one orbits, Japan J. Math. 3 (1977) 141-189.
30. F. Uchida, An orthogonal transformation group of the 8(k — 1)-sphere, J. Diff. Geom. 15 (1980) 569-574.
31. L. Verdiani, Cohomogeneity one Riemannian manifolds of even dimension with strictly positive curvature, I, Math. Z 241 (2002) 329-339.
32. N. Wallach, Compact homogeneous Riemannian manifolds with strictly positive curvature, Ann. Math. 96 (1972) 277-295.
33. B. Wilking, Group actions and manifolds of positive sectional curvature, Ufg, Goiania, 2002.
34. B. Wilking, Positively curved manifolds with symmetry, preprint.
35. B. Wilking, Torus actions on manifolds of positive sectional curvature, Acta Math. 191 (2003) 259-297.