Not every conjugate point of a semi-Riemannian geodesic is a bifurcation point

2017/03/30 by Giacomo Marchesi, Алессандро Порталури, Alessandro Portaluri +4
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Morphological variations and asymmetry #math-ph #math.DG #math.DS #math.MP

paper · pdf · doi:10.48550/arxiv.1703.10483

arxiv created 2017/03/30 · openalex publication_date 2017/03/30 · arxiv updated 2017/03/31 · openalex created_date 2022/08/29 · openalex updated_date 2026/07/28

Abstract

We revisit an example of a semi-Riemannian geodesic that was discussed by Musso, Pejsachowicz and Portaluri in 2007 to show that not every conjugate point is a bifurcation point. We point out a mistake in their argument, showing that on this geodesic actually every conjugate point is a bifurcation point. Finally, we provide an improved example which yields that the claim in our title is nevertheless true.

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