Codimension two complete noncompact submanifolds with nonnegative curvature

Noronha, Maria Helena

doi:10.1090/S0002-9947-1989-0978374-2

Codimension two complete noncompact submanifolds with nonnegative curvature
HTML articles powered by AMS MathViewer

by Maria Helena Noronha PDF

Trans. Amer. Math. Soc. 311 (1989), 739-748 Request permission

Abstract:

We study the topology of complete noncompact manifolds with non-negative sectional curvatures isometrically immersed in Euclidean spaces with codimension two. We investigate some conditions which imply that such a manifold is a topological product of a soul by a Euclidean space and this gives a complete topological description of this manifold.

References

Stephanie Alexander, Reducibility of Euclidean immersions of low codimension, J. Differential Geometry 3 (1969), 69–82. MR 250228
Yuriko Y. Baldin and Francesco Mercuri, Isometric immersions in codimension two with nonnegative curvature, Math. Z. 173 (1980), no. 2, 111–117. MR 583380, DOI 10.1007/BF01159953
Yuriko Y. Baldin and Francesco Mercuri, Codimension two nonorientable submanifolds with nonnegative curvature, Proc. Amer. Math. Soc. 103 (1988), no. 3, 918–920. MR 947682, DOI 10.1090/S0002-9939-1988-0947682-8
Yuriko Y. Baldin and Maria Helena Noronha, Some complete manifolds with nonnegative curvature operator, Math. Z. 195 (1987), no. 3, 383–390. MR 895308, DOI 10.1007/BF01161763
Richard L. Bishop, The holonomy algebra of immersed manifolds of codimension two, J. Differential Geometry 2 (1968), 347–353. MR 243460
Jeff Cheeger and Detlef Gromoll, On the structure of complete manifolds of nonnegative curvature, Ann. of Math. (2) 96 (1972), 413–443. MR 309010, DOI 10.2307/1970819
Philip Hartman, On the isometric immersions in Euclidean space of manifolds with nonnegative sectional curvatures. II, Trans. Amer. Math. Soc. 147 (1970), 529–540. MR 262981, DOI 10.1090/S0002-9947-1970-0262981-4
John Douglas Moore, Isometric immersions of riemannian products, J. Differential Geometry 5 (1971), 159–168. MR 307128
Richard Sacksteder, On hypersurfaces with no negative sectional curvatures, Amer. J. Math. 82 (1960), 609–630. MR 116292, DOI 10.2307/2372973
Alan Weinstein, Positively curved $n$-manifolds in $R^{n+2}$, J. Differential Geometry 4 (1970), 1–4. MR 264562