|
A sphere theorem for odd-dimensional submanifolds of spheres
Author(s):
Theodoros
Vlachos
Journal:
Proc. Amer. Math. Soc.
130
(2002),
167-173.
MSC (2000):
Primary 53C40;
Secondary 53C20.
Posted:
May 2, 2001
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
We establish a topological sphere theorem from the point of view of submanifold geometry for odd-dimensional submanifolds  of a unit sphere. We give examples which show that our result is optimal. Moreover, we note the assumption that the dimension  is odd is essential.
References:
-
- 1.
- M. P. do Carmo and N. R. Wallach, Minimal immersions of spheres into spheres, Ann. of Math. (2) 93 (1971), 43-62. MR 43:4048
- 2.
- R. S. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom. 17 (1982), 255-306. MR 84a:53050
- 3.
- Th. Hasanis and Th. Vlachos, Ricci curvature and minimal submanifolds, Pacific J. Math., 197 (2001), 13-24.
- 4.
- H. B. Lawson and J. Simons, On stable currents and their application to global problems in real and complex geometry, Ann. of Math. (2) 98 (1973), 427-450. MR 48:2881
- 5.
- K. Shiohama and H. Xu, The topological sphere theorem for complete submanifolds, Compositio Math. 107 (1997), 221-232. MR 98i:53080
- 6.
- D. Sjerve, Homology spheres which are covered by spheres, J. London Math. Soc. (2) 6 (1973), 333-336. MR 46:9993
- 7.
- N. R. Wallach, Minimal immersions of symmetric spaces into spheres, "Symmetric spaces", Ed. Boothby and Weiss, Dekker, New York, 1972, pp. 1-40. MR 53:11545
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
53C40,
53C20.
Retrieve articles in all Journals with MSC
(2000):
53C40,
53C20.
Additional Information:
Theodoros
Vlachos
Affiliation:
Department of Mathematics, University of Ioannina, Ioannina 45110, Greece
Email:
tvlachos@cc.uoi.gr
DOI:
10.1090/S0002-9939-01-06096-8
PII:
S 0002-9939(01)06096-8
Keywords:
Ricci curvature,
mean curvature vector,
homology groups
Received by editor(s):
March 1, 2000
Received by editor(s) in revised form:
May 17, 2000
Posted:
May 2, 2001
Communicated by:
Wolfgang Ziller
Copyright of article:
Copyright
2001,
American Mathematical Society
|
Comments: webmaster@ams.org