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<p>In this paper, we investigate the geometric properties of the characteristic Jacobi operator on almost Kenmotsu 3-manifolds. First, we show that such manifolds cannot possess a characteristic Jacobi operator of parallel or cyclic-parallel type. In contrast, we classify almost Kenmotsu 3-manifolds admitting a cyclic semi-parallel characteristic Jacobi operator. In particular, every <i>H</i>-almost Kenmotsu 3-manifold satisfies the cyclic semi-parallel condition for the characteristic Jacobi operator. Moreover, we completely classify cyclic parallelism and cyclic semi-parallelism for the characteristic Jacobi operator in homogeneous almost Kenmotsu 3-manifolds.</p>

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Almost Kenmotsu 3-Manifolds with Cyclic Semi-parallel Characteristic Jacobi Operator

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  • 发表日期：

    2026年7月30日

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  • Ji-Eun Lee

摘要

In this paper, we investigate the geometric properties of the characteristic Jacobi operator on almost Kenmotsu 3-manifolds. First, we show that such manifolds cannot possess a characteristic Jacobi operator of parallel or cyclic-parallel type. In contrast, we classify almost Kenmotsu 3-manifolds admitting a cyclic semi-parallel characteristic Jacobi operator. In particular, every H-almost Kenmotsu 3-manifold satisfies the cyclic semi-parallel condition for the characteristic Jacobi operator. Moreover, we completely classify cyclic parallelism and cyclic semi-parallelism for the characteristic Jacobi operator in homogeneous almost Kenmotsu 3-manifolds.