no. 1
Properties of hypersurfaces which are characteristic for spaces of constant curvature
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 3, Tome 26 (1972) no. 1, pp. 233-245. 
@article{ASNSP_1972_3_26_1_233_0,
     author = {Kowalski, Old\v rich},
     title = {Properties of hypersurfaces which are characteristic for spaces of constant curvature},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {233--245},
     publisher = {Scuola normale superiore},
     volume = {Ser. 3, 26},
     number = {1},
     year = {1972},
     zbl = {0233.53009},
     mrnumber = {362156},
     language = {en},
     url = {archive.numdam.org/item/ASNSP_1972_3_26_1_233_0/}
}
Kowalski, Oldřich. Properties of hypersurfaces which are characteristic for spaces of constant curvature. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 3, Tome 26 (1972) no. 1, pp. 233-245. http://archive.numdam.org/item/ASNSP_1972_3_26_1_233_0/

[1] Cartan. E. - Leçons sur la géometrie des espaces de Riemann, Paris 1928. | JFM 54.0755.01

[2] Kobayashi S., Nomizu K. - Foundations of Differential Geometry, Vol. I, Intersc. Publ. New-York - London, 1963. | MR 152974 | Zbl 0119.37502

[3] Kobayashi S., Nomizu K. - Foundations of Differential Geometry, Vol. II, Intersc. Publ., New York - London - Sydney, 1969. | MR 238225 | Zbl 0175.48504

[4] Petrov A.Z. - Prostranstva Einsteina, GIZ Fiz.-mat., Moskva 1961 (Russian). | MR 141492

[5] Rozenfel'D B.A. - Neevklidovy geometrii, Gos. izd. tech.-teor. literatury, Noskva 1955 (Russian). | MR 72491

[6] Thomas T.Y. - Riemann spaces of class one and their characterization, Acta Mathematica, Vol. 67 (1936) pp. 169-211. | JFM 62.0862.04 | Zbl 0015.27304

[7] Fialkow A. - Conformal differential geometry of a subspace, Trans. Amer. Math. Soc. Vol. 56 (1944), pp. 309-433. | MR 11023 | Zbl 0063.01359

[8] Kulkarni R.S., - Curvature structures and conformal transformations, Bull. Amer. Math. Soc. 75 (1969), pp. 91-94. (MR 38 # 1628). | MR 233306 | Zbl 0192.58601