NEW CURVATURE TENSORS ALONG RIEMANNIAN SUBMERSIONS

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Ayar G., Akyol M. A.

Miskolc Mathematical Notes, vol.24, no.3, pp.1161-1184, 2023 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 24 Issue: 3
  • Publication Date: 2023
  • Doi Number: 10.18514/mmn.2023.4118
  • Journal Name: Miskolc Mathematical Notes
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.1161-1184
  • Keywords: concircular curvature tensor, conformal curvature tensor, conharmonic curvature tensor, M-projective curvature tensor, Riemannian submersion, Weyl projective curvature tensor
  • Open Archive Collection: AVESIS Open Access Collection
  • Uşak University Affiliated: No

Abstract

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 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.