- #1
mach4
- 7
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I have a manifold M=S^4 which is endowed with a physical metric g.
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!
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!