Abstract
The composition of conformal and projective mappings between Riemannian spaces that were at the same time harmonic had been studied by S. E. Stepanov,I. G. Shandra in 2003 and further developed in I. Hinterleitner’s Ph.D. thesis in 2009. Conformal and projective mappings of Riemannian spaces preserving certain tensors were studied by O. Chepurna in the 2012 Ph.D. thesis. We consider conformal and projective mappings of generalized Riemannian spaces in Eisenhart’s sense and find necessary and sufficient conditions for these mappings to preserve curvature, Ricci and traceless Ricci tensors and some of their linear combinations. Particularly, as an additional contribution to related results collected in the Ph.D. thesis by O. Chepurna, we find that the following result holds in the case of Riemannian spaces: if a conformal mapping f1 : M → M^ is preserving the traceless Ricci tensor and a projective mapping f2 : M^ → M is preserving the traceless Ricci tensor then the Yano tensor of concircular curvature is invariant with respect to the composition f3 = f1 ◦ f2 : M → M.
Published Version
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