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Projective Transformations of Pseudo-Riemannian Manifolds

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REFERENCES

  1. Ya.L. Shapiro,“On geodesic fields of higher-dimensional directions,”Dokl.Akad.Nauk SSSR,32, No.4,237–239(1941).

  2. Ya.L. Shapiro,“Geodesic fields of directions and projective systems of paths,”Mat.Sb.,36,No.1, 125–148(1955).

  3. G.I. Kruchkovich,“On motions in semireducible Riemannian spaces,”Usp.Mat.Nauk,12,No.6, 149–156(1957).

  4. V.F. Kagan,Subprojective Spaces [in Russian],Fizmatgiz, Moscow (1961).

  5. T. Levi-Civita,“Sulle trasformazioni delle equazioni dinamiche,”Ann.Mat.Pura Appl.,Ser.2,24, 255–300(1896).

  6. Ya.L. Shapiro,“Geodesic field of directions as a whole,”Izv.Vuzov,Mat.,No.4,103–111(1970).

  7. E. Cartan,Geometry of Riemannian Spaces [Russian translation],ONTI, Moscow-Leningrad (1930).

  8. F. Schur,“Über den Zusammenhang der Räume constanten Krümmungsmasses mit den projectivn Raumen,”Math. Ann.,27,537–567(1886).

  9. A.S. Solodovnikov and N.R. Kamyshanskii,“Poles of pseudo-Riemannian spaces,”Izv.Akad.Nauk SSSR,Ser.Mat.,39,No.5,1093–1129(1975).

    Google Scholar 

  10. N.R. Kamyshanskii and A.S. Solodovnikov,“Semireducible analytic spaces 'as a whole,'”Usp. Mat.Nauk,35,No.5,3–51(1980).

    Google Scholar 

  11. T. Maebashi,“Vector lds and space forms,”J.Fac.Sci.Hokkaido Univ.,15,62–92(1960).

  12. S. Ishihara and Y. Tashiro,“On Riemannian manifolds admitting a concircular transformation,” Math.J.Okayama Univ.,9,19–47(1959).

    Google Scholar 

  13. Y. Tashiro,“Complete Riemannian manifolds and som vector lds,”Trans.Amer.Math.Soc., 117,No.5,251–275(1965).

  14. Y. Yano,“Concircular geometry,I,II,III,IV,V,”Proc.Imp.Acad.Tokyo,16,195–200,354–360,442–448,505–511 (1940);ibid,18,446–451 (1942).

    Google Scholar 

  15. L. Bianchi,Lexioni di Geometrie Differentiele,Vol.II,Part II,Pisa (1903).

  16. Ya.L. Shapiro and V.A. Igoshin,“Singular points of a geodesic ld,”Izv.Vuzov,Mat.,No.9,79–82 (1984).

    Google Scholar 

  17. Ya.L. Shapiro and V.A. Igoshin,“Geod sic eld with singularities and a cell manifold,”Izv.Vuzov,Mat.,No.11,74–77(1984).

    Google Scholar 

  18. A. Bess,Manifolds All of Whose Geodesics Are Closed [Russian translation ],Mir, Moscow (1981).

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Aminova, A.V. Projective Transformations of Pseudo-Riemannian Manifolds. Journal of Mathematical Sciences 113, 367–470 (2003). https://doi.org/10.1023/A:1021041802041

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