“Christoffel Symbol of the Second Kind”的概念、定义、习题解题方法及翻译-数学辞典

单词

Christoffel Symbol of the Second Kind

释义

Christoffel Symbol of the Second Kind

Variously denoted or .


			(1)

where

is a Connection Coefficient and

is a Christoffel Symbol of the First Kind.

(2)

The Christoffel symbols are given in terms of the first Fundamental Form

, and

and

. If

, the Christoffel symbols of thesecond kind simplify to

(Gray 1993).

The following relationships hold between the Christoffel symbols of the second kind and coefficients of the firstFundamental Form,

(Gray 1993).

For a surface given in Monge's Form ,

(23)

See also Christoffel Symbol of the First Kind, Connection Coefficient, Gauss Equations

References

Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 160-167, 1985.

Gray, A. ``Christoffel Symbols.'' §20.3 in Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 397-400, 1993.

Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 47-48, 1953.

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