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The complete dynamics description of positively curved metrics in the Wallach flag manifold $\mathrm{SU}(3)/\mathrm{T}^2$
| العنوان: | The complete dynamics description of positively curved metrics in the Wallach flag manifold $\mathrm{SU}(3)/\mathrm{T}^2$ |
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| المؤلفون: | Cavenaghi, Leonardo F., Grama, Lino, Martins, Ricardo M., Novaes, Douglas D. |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Differential Geometry, Mathematics - Dynamical Systems, 53C23, 37C20, 14M15 |
| الوصف: | The family of invariant Riemannian manifolds in the Wallach flag manifold $\mathrm{SU}(3)/\mathrm{T}^2$ is described by three parameters $(x,y,z)$ of positive real numbers. By restricting such a family of metrics in the \emph{tetrahedron} $\cal{T}:= x+y+z = 1$, in this paper, we describe all regions $\cal R \subset \cal T$ admitting metrics with curvature properties varying from positive sectional curvature to positive scalar curvature, including positive intermediate curvature notion's. We study the dynamics of such regions under the \emph{projected Ricci flow} in the plane $(x,y)$, concluding sign curvature maintenance and escaping. In addition, we obtain some results for positive intermediate Ricci curvature for a path of metrics on fiber bundles over $\mathrm{SU}(3)/\mathrm{T}^2$, further studying its evolution under the Ricci flow on the base. Comment: 15 pages, 12 figures. arXiv admin note: text overlap with arXiv:2305.06119 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2307.06418 |
| رقم الانضمام: | edsarx.2307.06418 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |