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Low codimensional submanifolds of Euclidean space with nonnegative isotropic curvature


Authors: Francesco Mercuri and Maria Helena Noronha
Journal: Trans. Amer. Math. Soc. 348 (1996), 2711-2724
MSC (1991): Primary 53C40, 53C42
DOI: https://doi.org/10.1090/S0002-9947-96-01589-9
MathSciNet review: 1348153
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Abstract: In this paper we study compact submanifolds of Euclidean space with nonnegative isotropic curvature and low codimension. We determine their homology completely in the case of hypersurfaces and for some low codimensional conformally flat immersions.


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  • 1. Y.Baldin, F.Mercuri Isometric immersions in codimension two with nonnegative curvature , Math.Z. 173, (1980), 111-117. MR 83c:53061
  • 2. Y.Baldin, F.Mercuri Codimension two nonorientable submanifolds with nonnegative curvature, Proc.A.M.S 103, (1988), 918-920. MR 89h:53112
  • 3. M.Berger, Sur les groupes d'holonomie des variétés a connexion affine et des variétés riemannienes, Bull.Soc.Math.France 83, (1955), 279-310. MR 18:149a
  • 4. M.Berger, Sur les groupes d'holonomie homogenes des variétés riemannienes, C.R. Acad.Sci.Paris serie A 262, (1966), 1316. MR 34:746
  • 5. R.L.Bishop, The holonomy algebra of immersed manifolds of codimension two, J.Diff.Geom. 2, (1968), 347-353. MR 39:4782
  • 6. R.B.Brown, A.Gray Riemannian manifolds with holonomy group immersed Spin(9), Differential Geometry ( in honor of K.Yano), Kinokuniya, Tokyo, (1972), 41-59. MR 48:7159
  • 7. M do Carmo, Differential geometry of curves and surfaces, Prentice Hall, Inc., 1976. MR 52:15253
  • 8. M.do Carmo, M.Dajczer, F.Mercuri, Compact conformally flat hypersurfaces, Trans. A.M.S. 288, (1985), 189-203. MR 86b:53052
  • 9. A.Derdzinski, Self-dual Kähler manifolds and Einstein manifolds of dimension four, Composito Math. 49, (1983), 405-433. MR 84h:53060
  • 10. A.Derdzinski, F.Mercuri, M.H.Noronha Manifolds with pure nonnegative curvature operator, Bol.Soc.Bras.Matem. 18, (1987), 13-22. MR 90i:53046
  • 11. S.Gallot, D.Meyer, Opérateur de courbure et Laplacien des formes différentelles d'une variété Riemanniene, J.Math.Pures et Appl. 54, (1975), 285-304. MR 56:13128
  • 12. R.S. Kulkarni, Curvature structure and conformal transformations, J.Diff.Geom. 4 (1970), 425-451. MR 44:2173
  • 13. M.Micallef, J.D.Moore, Minimal two-spheres and the topology of manifolds with positive curvature on totally isotropic two-planes, Ann. of Math 127, (1988), 199-227. MR 89e:53088
  • 14. M.Micallef, M.Y.Wang Metrics with nonnegative isotropic curvature, Duke Math.J. 72, (1993), 649-672. MR 94k:53052
  • 15. J.D.Moore, Isometric immersions of Riemannian products, J.Diff.Geom. 5, (1971), 159-168. MR 46:6249
  • 16. J.D.Moore, Conformally flat submanifolds of Euclidean space, Math.Ann. 225, (1977), 89-97. MR 55:4048
  • 17. M.H.Noronha, A note on the first Betti number of submanifolds of nonnegative Ricci curvature in codimension two, Manuscr.Math.73, (1991), 335-339. MR 92h:53050
  • 18. M.H.Noronha, Some compact conformally flat manifolds with non-negative scalar curvature, Geometriae Dedicata 47, (1993), 255-268. MR 94f:53068
  • 19. M.H.Noronha, Self-duality and four manifolds with nonnegative curvature on totally isotropic two-planes, Michigan Math.J. 41, (1994), 3-12. MR 95e:53069
  • 20. W.Seaman, On manifolds with non-negative curvature on totally isotropic 2-planes, Trans. A.M.S. 338, (1993), 843-855. MR 93j:53053

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Additional Information

Francesco Mercuri
Affiliation: IMECC-UNICAMP, Universidade Estadual de Campinas, 13081-970, Campinas, SP, Brasil
Email: mercuri@ime.unicamp.br

Maria Helena Noronha
Affiliation: Department of Mathematics, California State University Northridge, California 91330-8183
Email: mnoronha@huey.csun.edu

DOI: https://doi.org/10.1090/S0002-9947-96-01589-9
Keywords: Isotropic curvature, Betti numbers, hypersurfaces, conformally flat manifolds
Received by editor(s): March 24, 1995
Additional Notes: The first author’s research was partially supported by CNPq, Brasil.
Article copyright: © Copyright 1996 American Mathematical Society

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