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December 2019 Principal Curvatures of Homogeneous Hypersurfaces in a Grassmann Manifold $\widetilde{\text{Gr}}_{ 3}(\text{Im}\mathbb{O})$ by the $G_2$-action
Kanako ENOYOSHI
Tokyo J. Math. 42(2): 571-584 (December 2019). DOI: 10.3836/tjm/1502179291

Abstract

We compute the principal curvatures of homogeneous hypersurfaces in a Grassmann manifold $\widetilde{\text{Gr}}_{ 3}(\text{Im}\mathbb{O})$ by the $G_2$-action. As applications, we show that there is a unique orbit which is an austere submanifold, and that there are just two orbits which are proper biharmonic homogeneous hypersurfaces. We also show that the austere orbit is a weakly reflective submanifold.

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Kanako ENOYOSHI. "Principal Curvatures of Homogeneous Hypersurfaces in a Grassmann Manifold $\widetilde{\text{Gr}}_{ 3}(\text{Im}\mathbb{O})$ by the $G_2$-action." Tokyo J. Math. 42 (2) 571 - 584, December 2019. https://doi.org/10.3836/tjm/1502179291

Information

Published: December 2019
First available in Project Euclid: 8 March 2019

zbMATH: 07209634
MathSciNet: MR4106593
Digital Object Identifier: 10.3836/tjm/1502179291

Subjects:
Primary: 53B25
Secondary: 53C35

Rights: Copyright © 2019 Publication Committee for the Tokyo Journal of Mathematics

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Vol.42 • No. 2 • December 2019
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