Riemann Solitons on Homogeneous Siklos Spacetimes

In this paper, we investigate the properties of Riemann solitons on homogeneous Siklos spacetimes. Siklos spacetimes, which are special solutions to Einstein’s equations with a wave‐like potential, provide a suitable setting for studying the geometric properties of Riemann solitons. We first introduce the geometric structure of these spaces and then examine the conditions for the existence of Riemann solitons in this context. Our results indicate that the existence of such solitons depends on specific symmetries and curvature properties of these homogeneous spaces. Finally, explicit examples are presented, and their relevance to gravitational physics is discussed.