Inequalities on Riemannian Warped Product Submersions for Vertical Casorati Curvatures

Erken I. K., MURATHAN C., Siddiqui A. N.

Mediterranean Journal of Mathematics, vol.20, no.2, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 2
  • Publication Date: 2023
  • Doi Number: 10.1007/s00009-023-02313-5
  • Journal Name: Mediterranean Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Keywords: Riemannian immersion, Riemannian submersion, warped product, vertical Casorati curvatures, Einstein manifold, MANIFOLDS
  • Bursa Uludag University Affiliated: Yes

Abstract

© 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.The first and second authors introduced Riemannian warped product submersions and discussed interesting fundamental geometric properties of such submersions in Küpeli Erken and Murathan, Results Math 76(1) (2021), https://doi.org/10.1007/s00025-020-01310-4. In the present paper, we extend this study to put light on the curvature properties of such submersions and then obtain optimal inequalities for Riemannian warped product submersions involving vertical Casorati curvatures. Also, we discuss under which conditions the equality case of inequality can hold with an example.