Weakly reflective submanifolds and austere submanifolds
Osamu IKAWA, Takashi SAKAI, and Hiroyuki TASAKI
Source: J. Math. Soc. Japan Volume 61, Number 2
(2009), 437-481.
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.
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Keywords: reflective submanifold; austere submanifold; symmetric space; $s$-representation; $R$-space
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jmsj/1242220718
Digital Object Identifier: doi:10.2969/jmsj/06120437
Zentralblatt MATH identifier: 05573646
Mathematical Reviews number (MathSciNet): MR2532897
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