Principal Curvatures of Homogeneous Hypersurfaces in a Grassmann Manifold $\widetilde{\text{Gr}}_{ 3}(\text{Im}\mathbb{O})$ by the $G_2$-action
| Autor: | Kanako Enoyoshi |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Mathematics::Complex Variables General Mathematics 010102 general mathematics Submanifold 01 natural sciences Action (physics) 53B25 53C35 Principal curvature Homogeneous Grassmannian 0103 physical sciences Biharmonic equation 010307 mathematical physics Mathematics::Differential Geometry 0101 mathematics Orbit (control theory) Mathematics::Symplectic Geometry Mathematics |
| Zdroj: | Tokyo J. Math. 42, no. 2 (2019), 571-584 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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