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arXiv · 2405.20345

Bifurcation and Local Rigidity of Homogeneous Solutions to the Yamabe Problem on Aloff-Wallach Spaces

Lino Anderson da Silva Grama·Kennerson Nascimento de Sousa Lima
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Abstract

We construct 1-parameter families of well-known solutions to the Yamabe problem defined on Aloff-Wallach Spaces to determine bifurcation instants for these homogeneous spaces by examining changes in the Morse index of these metrics as the parameter varies over the positive real numbers. A bifurcation point for such families is an accumulation point of other solutions to the Yamabe problem, while a local rigidity point is an isolated solution of this problem, i.e., it is not a bifurcation point.

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Lino Anderson da Silva Grama, Kennerson Nascimento de Sousa Lima. 2024-05-20. Bifurcation and Local Rigidity of Homogeneous Solutions to the Yamabe Problem on Aloff-Wallach Spaces. https://arxiv.org/abs/2405.20345

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