The purpose of this paper is to study anti-invariant Riemannian submersions from Sasakian manifolds onto Riemannian manifolds such that characteristic vector field is vertical or horizontal vector field. We first show that any anti-invariant Riemannian submersions from Sasakian manifold is not a Riemannian submersion with totally umbilical fiber. Then we introduce anti-invariant Riemannian submersions from Sasakian manifolds with totally contact umbilical fibers. We investigate the totally contact geodesicity of fibers of such submersions. Moreover, under this condition, we investigate Ricci curvature of anti-invariant Riemannian submersions from Sasakian manifolds onto Riemannian manifolds.

中文翻译：

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来自具有完全脐纤维的 Sasakian 流形的反不变黎曼浸没

本文的目的是研究从 Sasakian 流形到 Riemann 流形的反不变黎曼淹没，使得特征向量场是垂直或水平向量场。我们首先表明，任何来自 Sasakian 流形的反不变黎曼浸没都不是具有完全脐纤维的黎曼浸没。然后我们介绍了来自完全接触脐纤维的 Sasakian 流形的反不变黎曼浸没。我们研究了这种浸没的纤维的完全接触测地线。此外，在这种情况下，我们研究了从 Sasakian 流形到黎曼流形的反不变黎曼浸没的 Ricci 曲率。