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1591238460
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- Assume M=xdy -ydx+dz ∈ Ω1(R^3). What's the restriction of M to the plane {z=2}? I think it's xdy-ydx. Is that right?
Do the two forms have the same values on tangent vectors to z = 2?1591238460 said:
- Assume M=xdy -ydx+dz ∈ Ω1(R^3). What's the restriction of M to the plane {z=2}? I think it's xdy-ydx. Is that right?
Just check the values.1591238460 said:Thank you, so what should I do?
Use ## ##'s at the beginning and end if you want to do Latex editing here.1591238460 said:I think the tangent vectors of the plane z=2 are in the form of a$\frac{\partial}{\partial x}$+b$\frac{\partial}{\partial y}$, to a$\frac{\partial}{\partial x}$+b$\frac{\partial}{\partial y}$, both of the two forms of the value, am I right?
1591238460 said:I think the tangent vectors of the plane z=2 are in the form of a##\frac{\partial}{\partial x}+b\frac{\partial}{\partial y}##, to a ##\frac{\partial}{\partial x}+b\frac{\partial}{\partial y} ##, both of the two forms of the value, am I right?
The restriction of differential form is a mathematical concept that involves taking a differential form defined on a larger space and restricting it to a smaller subset of that space. It essentially involves narrowing the scope of the differential form to a specific region or domain.
The restriction of differential form is important because it allows us to study the behavior of a differential form in a more specific and manageable setting. It also enables us to apply differential forms to various physical systems and problems, making it a powerful tool in mathematical modeling and analysis.
A differential form is a mathematical object defined on a larger space, while its restriction is a version of that form that is only defined on a smaller subset of the space. The restriction may have different properties or behaviors compared to the original form, as it is limited to a specific region or domain.
The restriction of differential form is closely related to integration, as it allows us to integrate a form over a specific region or domain rather than the entire space. This is useful in solving problems that involve calculating the total effect or influence of a differential form on a specific area.
Yes, the restriction of differential form can be extended to higher dimensions. In fact, the concept of restriction is not limited to differential forms but can also be applied to other mathematical objects, such as functions and vector fields, in higher dimensions.