The Bour’s Theorem for Invariant Surfaces in Three-Manifolds

Key Points

• The research aims to establish a generalized Bour's theorem for surfaces under specific symmetry conditions in 3-manifolds.
• Applied techniques from equivariant geometry
• Analyzed the action of closed one-parameter groups of isometries
• Proved the theorem through geometric arguments
• Confirmed that the generalized Bour's theorem holds for the studied surfaces
• Expanded understanding of invariant surfaces within Riemannian geometry