A+ CATEGORY SCIENTIFIC UNIT

On some generalized Einstein metric conditions on hypersurfaces in semi-Riemannian space forms

Volume 96 / 2003

Ryszard Deszcz, Małgorzata Głogowska, Marian Hotloś, Leopold Verstraelen Colloquium Mathematicum 96 (2003), 149-166 MSC: 53B20, 53B25, 53B30, 53B50, 53C25, 53C40. DOI: 10.4064/cm96-2-1

Abstract

Solutions of the P. J. Ryan problem as well as investigations of curvature properties of Cartan hypersurfaces and Ricci-pseudosymmetric hypersurfaces lead to curvature identities holding on every hypersurface $M$ isometrically immersed in a semi-Riemannian space form. These identities, under some assumptions, give rises to new generalized Einstein metric conditions on $M$. We investigate hypersurfaces satisfying such curvature conditions.

Authors

  • Ryszard DeszczDepartment of Mathematics
    Agricultural University of Wrocław
    Grunwaldzka 53
    50-357 Wrocław, Poland
    e-mail
  • Małgorzata GłogowskaDepartment of Mathematics
    Agricultural University of Wrocław
    Grunwaldzka 53
    50-357 Wrocław, Poland
    e-mail
  • Marian HotlośInstitute of Mathematics
    Wrocław University of Technology
    Wybrzeże Wyspiańskiego 27
    50-370 Wrocław, Poland
    e-mail
  • Leopold VerstraelenDepartment of Mathematics
    Katholieke Universiteit Leuven
    Celestijnenlaan 200B
    B-3001 Leuven, Belgium
    e-mail

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