Geodesic
Smoothness of a hypersurface of positive extrinsic curvature and its fundamental forms in conjugate-harmonic coordinates
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (1982), pp. 5-8 
I. Kh. Sabitov. Smoothness of a hypersurface of positive extrinsic curvature and its fundamental forms in conjugate-harmonic coordinates. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (1982), pp. 5-8. http://geodesic.mathdoc.fr/item/VMUMM_1982_6_a1/
@article{VMUMM_1982_6_a1,
     author = {I. Kh. Sabitov},
     title = {Smoothness of a hypersurface of positive extrinsic curvature and its fundamental forms in conjugate-harmonic coordinates},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {5--8},
     year = {1982},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_1982_6_a1/}
}
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We show that the regularity of the surface and its forms as in the title coincides with the regularity of the second fundamental form of the surface.