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Codimension two Kähler submanifolds of space forms

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Abstract

In this article we study isometric immersions from Kähler manifolds whose (1, 1) part of the second fundamental form is parallel, theppmc isometric immersions. When the domain is a Riemann surface these immersions are precisely those with parallel mean curvature. P. J. Ryan has classified the Kähler manifolds that admit isometric immersions, as real hypersurfaces, in space forms. We classify the codimension twoppmc isometric immersions into space forms.

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Authors and Affiliations

  1. Departamento de Matemática Faculdade de Ciências, Universidade de Lisboa, R. Ernesto de Vasconcelos, C1, 3°, 1749-016, Lisboa, Portugal

    M. J. Ferreira

  2. Instituto de Matemática, ICE, Universidade do Amazonas, 6900, AM, Manaus, Brasil

    R. Tribuzy

Authors
  1. M. J. Ferreira
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  2. R. Tribuzy
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Additional information

Work supported by FCT, Praxis XXI, Feder, project Praxis/2/2.1/MAT/125/94 (Ferreira), CNPq, Brasil and ICTP, Italy (Tribuzy).

Eine überarbeitete Fassung ging am 21. 3. 2001 ein

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Ferreira, M.J., Tribuzy, R. Codimension two Kähler submanifolds of space forms. Arch. Math 79, 520–528 (2002). https://doi.org/10.1007/BF02638390

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  • DOI: https://doi.org/10.1007/BF02638390

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