Open Access
April, 2009 Weakly reflective submanifolds and austere submanifolds
Osamu IKAWA, Takashi SAKAI, Hiroyuki TASAKI
J. Math. Soc. Japan 61(2): 437-481 (April, 2009). DOI: 10.2969/jmsj/06120437


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.


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Osamu IKAWA. Takashi SAKAI. Hiroyuki TASAKI. "Weakly reflective submanifolds and austere submanifolds." J. Math. Soc. Japan 61 (2) 437 - 481, April, 2009.


Published: April, 2009
First available in Project Euclid: 13 May 2009

zbMATH: 1187.53058
MathSciNet: MR2532897
Digital Object Identifier: 10.2969/jmsj/06120437

Primary: 53C40
Secondary: 53C35

Keywords: $R$-space , $s$-representation , austere submanifold , reflective submanifold , Symmetric space

Rights: Copyright © 2009 Mathematical Society of Japan

Vol.61 • No. 2 • April, 2009
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