Geometry and topology of submanifolds immersed in space forms and ellipsoids

DOI 2 Citations 5 References
  • Zhang Xue-Shan
    DEPARTMENT OF MATHEMATICS XIAN UNIVERSITY OF ARCHITECTURE AND TECHNOLOGY

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Description

Let Mm be a compact submanifold of a simply connected space form Nn(c) with c{≥}0. Denote by s and H the square length of the second fundamental form and the mean curvature vector field of M respectively. By introducing a selfadjoint linear operator QA associated with the shape operator of M, we show that there are no stable currents in M and topologically, M is a sphere if s<H2/(m−1). For an immersed submanifold of the ellipsoid we show that appropriate assumption on QA implies the vanishing of a given homology group.

Journal

  • Kodai Mathematical Journal

    Kodai Mathematical Journal 17 (2), 262-272, 1994

    Institute of Science Tokyo, Department of Mathematics

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Details 詳細情報について

  • CRID
    1390282680249873920
  • NII Article ID
    130003574181
  • DOI
    10.2996/kmj/1138039965
  • ISSN
    18815472
    03865991
  • MRID
    1282215
  • Text Lang
    en
  • Data Source
    • JaLC
    • Crossref
    • CiNii Articles
  • Abstract License Flag
    Disallowed

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