Artículos de revistas
Codimension Three Nonnegatively Curved Submanifolds With Infinite Fundamental Group
Registro en:
Mathematische Zeitschrift. , v. 267, n. 1, p. 403 - 411, 2011.
255874
10.1007/s00209-009-0625-5
2-s2.0-79551605559
Autor
Foss J.N.
DeMartino M.
Noronha M.H.
Santos G.
Institución
Resumen
We show that a complete, codimension three submanifold M of nonnegative sectional curvature that isometrically splits as M̄ × ℝ has nonnegative curvature operator. We apply this result to obtain a classification of codimension three nonflat manifolds of nonnegative sectional curvature and infinite fundamental group. © 2009 Springer-Verlag. 267 1 403 411 Baldin, Y., Mercuri, F., Isometric immersions in codimension two with nonnegative curvature (1980) Math. Z., 173, pp. 111-117 Baldin, Y., Mercuri, F., Two nonorientable submanifolds with nonnegative curvature (1988) Proc. AMS, 103, pp. 918-920 Bishop, R.L., The holonomy algebra of immersed manifolds of codimension two (1971) J. Differ. Geom, 6, pp. 119-128 Böhm, C., Wilking, B., Manifolds with positive curvature operators are space forms (2008) Ann. Math, 167 (2-3), pp. 1079-1097 Cheeger, J., Gromoll, D., On the structure of complete manifolds of nonnegative curvature (1972) Ann. Math, 96 (2), pp. 413-443 Dajczer, M., (1990) Submanifolds and Isometric Immersions. Mathematics Lecture Series 13, , Houston: Publish or Perish Inc Guijarro, L., Isometric Immersions without Positive Ricci Curvature, Contemporary Mathematics, Global differential geometry: The Mathematical Legacy of Alfred Gray (Bilbao, 2000) (2001) Contemporary Mathematics, 288, pp. 339-342. , American Mathematical Society, Providence Hamilton, R., Four-manifolds with positive curvature operator (1986) J. Differ. Geom, 24, pp. 153-179 Hartman, P., On the isometric immersion in Euclidean space of manifolds with nonnegative sectional curvatures (1970) Trans. AMS, 147, pp. 529-540 Kleinjohann, N., Walter, R., Nonnegativity of the Curvature Operator and Isotropy for Isometric Immersions (1982) Math. Z, 181, pp. 129-142 Mercuri, F., Noronha, M.H., On the topology of complete Riemannian manifolds with nonnegative curvature operator (1993) Rendiconti Semin. Facolta Sci. Univ. Cagliari., 63, pp. 1-23 Micallef, M., Moore, J.D., Minimal two-spheres and the topology of manifolds with positive curvature on totally isotropic two-planes (1988) Ann. Math., 127, pp. 199-227 Noronha, M.H., A splitting theorem for complete manifolds with nonnegative curvature operator (1989) Proc. AMS, 105, pp. 979-985 Noronha, M.H., Nonnegatively curved submanifolds in codimension two (1992) Trans. AMS, 332, pp. 351-364 Siu, Y.T., Yau, S.T., Compact Kähler manifolds with positive bisectional curvature (1980) Invent. Math, 59, pp. 189-204 Toponogov, V.A., Spaces with straight lines (1964) Am. Math. Soc. Trans., 37, pp. 287-290 Weinstein, A., Positively curved n-manifolds in ℝn+2 (1970) J. Differ. Geom, 4, pp. 1-4