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In that example, the base space of a fiber bundle is pulled back, in the sense of precomposition, above. The fibers then travel along with the points in the base space at which they are anchored: the resulting new pullback bundle looks locally like a Cartesian product of the new base space, and the (unchanged) fiber.
More generally, any covariant tensor field – in particular any differential form – on may be pulled back to using . When the map ϕ {\displaystyle \phi } is a diffeomorphism , then the pullback, together with the pushforward , can be used to transform any tensor field from N {\displaystyle N} to M {\displaystyle M} or vice versa.
These relationships differ from non-cyclical relationships in that on-again, off-again relationships are between partners that have pre-existing knowledge and experiences with each other. [4] In addition to this, on-and-off partners often report more relationship uncertainty, questioning the meaning of the relationship, its strength, and future ...
Relationship lost its spark? These experts say it’s normal for long-term love to feel like it’s flaming out, and gave us these tips to fall in love again.
Narcissist at the end of a relationship with their partner. You came. You saw. You dated a narcissist. You're over it—or perhaps you have a sneaking suspicion that they are over you.
Crab mentality, also known as crab theory, [1] [2] crabs in a bucket [a] mentality, or the crab-bucket effect, is a mentality of which people will try to prevent others from gaining a favourable position in something, even if it has no effect on those trying to stop them.
A relationship breakup, breakup, [1] or break-up [2] is the ending of a relationship.The act is commonly termed "dumping [someone]" in slang when it is initiated by one partner.
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