- #1
Manicwhale
- 10
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I'm reading Hawking and Ellis, and on p.16 they say that
"The subspace of T_p defined by \langle \omega,x \rangle=(constant) for a given one-form \omega, is linear."
But in what sense is this true? For if the constant is non-zero, the 0 of T_p is not in the subspace, nor does it satisfy the usual linearity condition.
By analogy with euclidean space, the points r \cdot a = d form a plane, but not technically a subspace of the original space (since it is "shifted"). Am I missing something?
"The subspace of T_p defined by \langle \omega,x \rangle=(constant) for a given one-form \omega, is linear."
But in what sense is this true? For if the constant is non-zero, the 0 of T_p is not in the subspace, nor does it satisfy the usual linearity condition.
By analogy with euclidean space, the points r \cdot a = d form a plane, but not technically a subspace of the original space (since it is "shifted"). Am I missing something?
