I have a manifold M=S^4 which is endowed with a physical metric g.(adsbygoogle = window.adsbygoogle || []).push({});

I can define another metric on this manifold h (a pullback metric).

Does it make sense to define a one-parameter family of metrics G(u) on the manifold M in the form

G(u) = (1-u)*g + u*h , where u is a parameter in [0,1] ?

Are there any compatibility conditions?

Any help would be appreciated - Thx!

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# One-parameter family of metrics

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