EQUICENTRO-AFFINE MAXIMAL SPACELIKE ISOPARAMETRIC HYPERSURFACES

This paper investigates compact equicentro-affine maximal spacelike isoparametric hypersurfaces in de Sitter space S n+1 1 and hyperbolic space H n+1 .By analyzing the evolution of invariant submanifold flows under equicentro-affine unimodular transformations, we derive the first variation formulas for the equicentro-affine invariant area.Depending on whether the Euler-Lagrange operator is zero or constant, we split the problem into non-generalized and generalized cases, and arrived at the same second variation formula.Subsequently, we discuss these two isoparametric cases separately.Stability analysis shows, however, that no maximal hypersurface exists in the former scenario.For the latter, a complete classification is provided, with and without boundary assumptions.Moreover, explicit curvature expressions are obtained for a subclass of generalized maximal hypersurfaces.