Weakly reflective submanifolds and austere submanifolds

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Author(s)

Abstract

An austere submanifold is a minimal submanifold where for each normal vector, the set of eigenvalues of its shape operator is invariant under the multiplication by −1. In the present paper, we introduce the notion of weakly reflective submanifold, which is an austere submanifold with a reflection for each normal direction, and study its fundamental properties. Using these, we determine weakly reflective orbits and austere orbits of linear isotropy representations of Riemannian symmetric spaces.

Journal

  • Journal of the Mathematical Society of Japan

    Journal of the Mathematical Society of Japan 61(2), 437-481, 2009-04-01

    The Mathematical Society of Japan

References:  14

Cited by:  1

Codes

  • NII Article ID (NAID)
    10024905762
  • NII NACSIS-CAT ID (NCID)
    AA0070177X
  • Text Lang
    ENG
  • Article Type
    Journal Article
  • ISSN
    00255645
  • NDL Article ID
    10207807
  • NDL Source Classification
    ZM31(科学技術--数学)
  • NDL Call No.
    Z53-A209
  • Data Source
    CJP  CJPref  NDL  J-STAGE 
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