Tensor foundations of tunnel mathematics

Abstract The main relations of tunnel mathematics (theory of functions of spatial complex variable) can be obtained with the aid of tensor analysis. It is commonly known, for instance, that a second-rank tensor being multiplied by vector on a plane can change a direction of this vector, i. e. second-rank tensor can take the vector out of the plane. Besides, tunnel mathematics can be applied for solving problems of fluid dynamics and theory of elasticity where tensor analysis is used very broadly. So, it is naturally to use tensor analysis for building the tunnel mathematics.