Definition:Covariant Tensor

Definition

Let $F$ be a tensor of type $\tuple {k, 0}$:

$\ds F : \underbrace{V \times \ldots \times V}_{\text{$k$ times}} \to \R$

Then $F$ is called a covariant $k$-tensor (on $V$).

Also see

• Results about covariant tensors can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): covariant tensor
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): covariant tensor
• 2018: John M. Lee: Introduction to Riemannian Manifolds (2nd ed.): Appendix $\text B$. Review of Tensors