A Cartesian tensor is a tensor in three-dimensional Euclidean space. Unlike general tensors, there is no distinction between covariant and contravariant indices for Cartesian tensors. However, tensors in non-Euclidean spaces (e.g., Lorentzian spaces) do require this distinction.
Cartesian Tensor
See also
Affine Tensor, Contravariant Tensor, Covariant Tensor, TensorExplore with Wolfram|Alpha
References
Arfken, G. "Tensor Analysis." Ch. 3 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 118-167, 1985.Goldstein, H. Classical Mechanics, 2nd ed. Reading, MA: Addison-Wesley, p. 192, 1980.Jeffreys, H. Cartesian Tensors. Cambridge: The University Press, 1931.Lovelock, D. and Rund, H. Tensors, Differential Forms, and Variational Principles. New York: Dover, 1989.Synge, J. L. and Schild, A. Tensor Calculus. New York: Dover, pp. 127-136, 1978.Referenced on Wolfram|Alpha
Cartesian TensorCite this as:
Weisstein, Eric W. "Cartesian Tensor." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CartesianTensor.html