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The manifold of essential matrices is equipped with a one-parameter family of (pseudo-)Riemannian metrics. For the whole family, explicit formulas for geodesics are derived. Moreover, specific curves, so-called quasi-geodesics, are studied and a closed form expression for a quasi-geodesic connecting two given essential matrices is obtained.

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A Family of Metrics and Quasi-geodesics on the Manifold of Essential Matrices

  • 会议论文

  • 发表日期：

    2025年

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  • Markus Schlarb

摘要

The manifold of essential matrices is equipped with a one-parameter family of (pseudo-)Riemannian metrics. For the whole family, explicit formulas for geodesics are derived. Moreover, specific curves, so-called quasi-geodesics, are studied and a closed form expression for a quasi-geodesic connecting two given essential matrices is obtained.