Journal of the Mathematical Society of Japan

Weakly reflective submanifolds and austere submanifolds

Osamu IKAWA, Takashi SAKAI, and Hiroyuki TASAKI

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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.

Article information

J. Math. Soc. Japan, Volume 61, Number 2 (2009), 437-481.

First available in Project Euclid: 13 May 2009

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Zentralblatt MATH identifier

Primary: 53C40: Global submanifolds [See also 53B25]
Secondary: 53C35: Symmetric spaces [See also 32M15, 57T15]

reflective submanifold austere submanifold symmetric space $s$-representation $R$-space


IKAWA, Osamu; SAKAI, Takashi; TASAKI, Hiroyuki. Weakly reflective submanifolds and austere submanifolds. J. Math. Soc. Japan 61 (2009), no. 2, 437--481. doi:10.2969/jmsj/06120437.

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