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Projective Curvature Tensors of Some Special Manifolds with Non-symmetric Linear Connection


We consider geodesic mappings between some special manifolds with the non-symmetric linear connection. We obtain some tensors that are invariant with respect to geodesic mappings by relaxing the so-called “equitorsion condition”. Derived tensors have algebraic expressions analogous to the Weyl tensor of projective curvature, apart from that the generalized Ricci and curvature tensors appeared instead of the usual Ricci and curvature tensors. Further, we study some properties of mentioned invariant tensors as well as their relations with the Weyl tensor of projective curvature. Finally, we introduce some kinds of recurrent manifolds with the non-symmetric linear connection as well as their generalized Ricci and projective counterparts.

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The authors wish to express their gratitude to referees for several useful comments that improved the readability of the paper. The research by Miloš Z. Petrović leading to these results was partially supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia, project no. 174012.

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Correspondence to Miloš Z. Petrović.

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Dedicated to Professor Svetislav Minčić on the occasion of his 90th birthday.

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Petrović, M.Z., Velimirović, A.M. Projective Curvature Tensors of Some Special Manifolds with Non-symmetric Linear Connection. Mediterr. J. Math. 18, 124 (2021).

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  • Geodesic mapping
  • Weyl projective curvature
  • non-symmetric linear connection
  • torsion
  • invariant

Mathematics Subject Classification

  • Primary 53B05
  • Secondary 53B20
  • 53C15