Bifurcation and local rigidity of homogeneous solutions to the Yamabe problem on Aloff-Wallach spaces

Journal of Differential Equations 2026 Open access

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Authors: Lino Grama, Kennerson N. S. Lima
DOI: 10.1016/j.jde.2026.114707
Cited by: 0
References: 22

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.

Fields of Study & Subjects

Advanced Mathematical Modeling in Engineering Differential Equations and Numerical Methods Differential Equations and Boundary Problems

Publication details

Journal / source
Journal of Differential Equations
Publisher
Elsevier BV
Volume
482
Pages
114707–114707
Publication date
17 August 2026
Language
EN