On the determination of shifting operators along geodesics on a surface

Abstract

A procedure to obtain a closed form of the shifting operators along a known geodesic line on a surface as a solution of a system of linear algebraic equations is proposed. Its correctness is numerically demonstrated in the case of a helicoid surface and a spherical one. The future use of these operators in finite element approximations of tensor fields in non-Euclidean spaces is announced.

Keywords

• surface
• geodesic line
• parallel transport
• shifting operators