(1) | |||

(2) |

where , , and are coefficients of the second Fundamental Form and are Christoffel Symbols of the Second Kind. Therefore,

(3) | |||

(4) |

(5) | |||

(6) |

(7) | |||

(8) |

where , , and are coefficients of the first Fundamental Form.

**References**

Gray, A. ``The Mainardi-Codazzi Equations.'' §20.4 in
*Modern Differential Geometry of Curves and Surfaces.* Boca Raton, FL: CRC Press, pp. 401-402, 1993.

© 1996-9

1999-05-26