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On the characteristic Jacobi operator of the unit tangent sphere bundles over surfaces

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We prove that the characteristic Jacobi operator $\ell$ of the unit tangent sphere bundle over a surface is properly pseudo-parallel when and only when the base surface is of constant curvature $1$ or $4/3$. The latter case only occurs for $2$-dimensional base manifolds.

Abstract

We prove that the characteristic Jacobi operator $\ell$ of the unit tangent sphere bundle over a surface is properly pseudo-parallel when and only when the base surface is of constant curvature $1$ or $4/3$. The latter case only occurs for $2$-dimensional base manifolds.

참고문헌 (23)

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