New curvature tensors along Riemannian submersions

Gülhan Ayar; Mehmet Akif Akyol;


In 1966, B. O’Neill [The fundamental equations of a submersion, Michigan Math. J.,Volume 13, Issue 4 (1966), 459-469.] defined some fundamental equations and curvature relations between the total space, the base space and the fibres on a submersion. In the present paper,we define new curvature tensors on Riemannian submersions such as Weyl projective curvature tensor, concircular curvature tensor, conharmonic curvature tensor, conformal curvature tensorand 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.

Vol. 24 (2023), No. 3, pp. 1161-1184
DOI: 10.18514/MMN.2023.4118

Download: MMN-4118