Differentiating Unit Orthogonal Vectors in a Riemannian Space that Admits an N-tuply Orthogonal System of Hypersurfaces

Details Differentiating Unit Orthogonal Vectors in a Riemannian Space that Admits an N-tuply Orthogonal System of Hypersurfaces Differentiating Unit Orthogonal Vectors in a Riemannian Space that Admits an N-tuply Orthogonal System of Hypersurfaces

Mar 1967

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1967amjph..35..271w&link_type=abstract

American Journal of Physics, Volume 35, Issue 3, pp. 271-273 (1967).

Physics

Scientific paper

In a normal coordinate system { ya } , the identity ∂2xp/∂yn∂ym = ∂2xp/∂ym∂yn is used to obtain expressions, involving the components of the metric tensor in this coordinate system, for the derivatives of the unit tangent vectors to the parametric curves. An example is given for a normal coordinate system in the De Sitter universe.

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