Bulk contraction and Duals: Difference between pages
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Eric Lengyel (talk | contribs) (Created page with "The ''metric dual'' or just "dual" of an object $$\mathbf u$$ is denoted by $$\mathbf u^\unicode["segoe ui symbol"]{x2605}$$ and defined as :$$\mathbf u^\unicode["segoe ui symbol"]{x2605} = \overline{\mathbf{Gu}}$$ , where $$\mathbf G$$ is the extended metric tensor. The ''metric antidual'' or just "antidual" of an object $$\mathbf u$$ is denoted by $$\mathbf u^\unicode["segoe ui symbol"]{x2606}$$ and defined as :$$\mathbf u^\unicode["segoe ui symbol"]{x2606} = \over...") |
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The ''metric dual'' or just "dual" of an object $$\mathbf u$$ is denoted by $$\mathbf u^\unicode["segoe ui symbol"]{x2605}$$ and defined as | |||
:$$\mathbf u^\unicode["segoe ui symbol"]{x2605} = \overline{\mathbf{Gu}}$$ , | |||
where $$\mathbf G$$ is the extended metric tensor. | |||
The ''metric antidual'' or just "antidual" of an object $$\mathbf u$$ is denoted by $$\mathbf u^\unicode["segoe ui symbol"]{x2606}$$ and defined as | |||
:$$\mathbf u^\unicode["segoe ui symbol"]{x2606} = \overline{\mathbb G \mathbf u}$$ , | |||
where $$\mathbb G$$ is the extended antimetric tensor. | |||
Revision as of 06:15, 12 April 2024
The metric dual or just "dual" of an object $$\mathbf u$$ is denoted by $$\mathbf u^\unicode["segoe ui symbol"]{x2605}$$ and defined as
- $$\mathbf u^\unicode["segoe ui symbol"]{x2605} = \overline{\mathbf{Gu}}$$ ,
where $$\mathbf G$$ is the extended metric tensor.
The metric antidual or just "antidual" of an object $$\mathbf u$$ is denoted by $$\mathbf u^\unicode["segoe ui symbol"]{x2606}$$ and defined as
- $$\mathbf u^\unicode["segoe ui symbol"]{x2606} = \overline{\mathbb G \mathbf u}$$ ,
where $$\mathbb G$$ is the extended antimetric tensor.