Bifurcation and local rigidity of homogeneous solutions to the Yamabe problem on Aloff-Wallach spaces
Lino Grama, Kennerson N. S. Lima · Journal of Differential Equations · 2026
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.