论文标题
Riemannian浸没的新曲率张量
New curvature tensors along Riemannian submersions
论文作者
论文摘要
1966年，B。O'Neill[淹没的基本方程，密歇根州数学。 J.，第13卷，第4期（1966），459-469。在本文中，我们分别定义了沿riemannian浸没的新曲率张量，例如Weyl弹性曲率张量，偶发曲率张量，凸曲率曲率张量，保形曲率张量和$ M- $ m- $ m- $ j弹性曲率张量。最后，我们获得了一些结果，如果利曼浸没的总空间具有上述任何曲率张量的脐带纤维。
In 1966, B. O'Neill [The fundamental equations of a submersion, Michigan Math. J., Volume 13, Issue 4 (1966), 459-469.] obtained some fundamental equations and curvature relations between the total space, the base space and the fibres of a submersion. In the present paper, we define new curvature tensors along Riemannian submersions such as Weyl projective curvature tensor, concircular curvature tensor, conharmonic curvature tensor, conformal curvature tensor and $M-$projective curvature tensor, respectively. Finally, we obtain some results in case of the total space of Riemannian submersions has umbilical fibres for any curvature tensors mentioned by the above.
