Geodesic
On local automorphisms of real analytic hypersurfaces
Izvestiya. Mathematics , Tome 18 (1982) no. 3, pp. 537-559.

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In this paper the author studies biholomorphic transformations of $\mathbf C^n$ carrying a nondegenerate real analytic surface $M$ into itself and leaving a particular point $\xi\in M$ fixed. The first estimates of the dimensions of such groups of transformations were obtained by V. K. Beloshapka (see Izv. Akad. Nauk SSSR Ser. Mat., 1979, v. 43, № 2, pp. 243–266). In the present paper it is proved that the dimension of such groups for a nonspherical surface $M$ does not exceed $(n-1)^2$. Bibliography: 2 titles. 
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A. V. Loboda. On local automorphisms of real analytic hypersurfaces. Izvestiya. Mathematics , Tome 18 (1982) no. 3, pp. 537-559. http://geodesic.mathdoc.fr/item/IM2_1982_18_3_a6/

[1] Beloshapka V. K., “O razmernosti gruppy avtomorfizmov analiticheskoi giperpoverkhnosti”, Izv. AN SSSR. Ser. matem., 43:2 (1979), 243–266 | MR | Zbl

[2] Chern S. S., Moser J. K., “Real Hypersurfaces in Complex Manifolds”, Acta Math., 133:3 (1974), 219–271 | DOI | MR