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New curvature tensors along Riemannian submersions
- Publication Year :
- 2020
-
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.<br />Comment: 24 pages
- Subjects :
- Mathematics - General Mathematics
53C15, 53B20
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2007.07814
- Document Type :
- Working Paper