Recurrent-Flag Rigidity under Pure Axial Torsion

Key Points

• The study aims to establish the relationship between pure axial torsion and the projective recurrence locus of principal spinor flags in four-dimensional Lorentzian geometry.
• Analyzed the effects of axial torsion on principal spinor flags
• Separated different aspects of recurrence including connection recurrence and Frobenius integrability
• Presented a non-Einstein Kundt example with a recurrent principal flag
• Demonstrated that pure axial torsion does not change the projective recurrence locus
• Clarified separations among connection recurrence, Frobenius integrability, and spinor identities
• Provided evidence of recurrent principal flag using a non-Einstein Kundt example