New curvature tensors along Riemannian submersions

2020/07/13 by Mehmet Akif Akyol, Akyol, Mehmet Akif, Gülhan Ayar +1
Mathematics · #53B20 #53C15 #FOS: Mathematics #General Mathematics (math.GM) #math.GM #msc:53B20 #msc:53C15

paper · pdf · doi:10.48550/arxiv.2007.07814

24 pages

arxiv created 2020/07/13 · arxiv updated 2020/07/16

Abstract

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.

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