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<p>We study Hessian geometry on warped product manifolds. In particular, we consider the case where the fiber space of the warped product is a Hessian manifold and the base space is an interval. For a given Hessian potential on the fiber space and some warping functions, we find an explicit formula for a Hessian potential and the affine coordinate systems on the warped product manifold. Moreover, we consider the obtained formula from the viewpoint of equiaffine differential geometry.</p>

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An explicit formula for Hessian potentials on warped product manifolds

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年9月5日

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  • Tatsuo Suzuki

摘要

We study Hessian geometry on warped product manifolds. In particular, we consider the case where the fiber space of the warped product is a Hessian manifold and the base space is an interval. For a given Hessian potential on the fiber space and some warping functions, we find an explicit formula for a Hessian potential and the affine coordinate systems on the warped product manifold. Moreover, we consider the obtained formula from the viewpoint of equiaffine differential geometry.