I What is the hyper-cylindrical line element?

Caroline
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What is the hyper-cylindrical line element?
 
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Caroline said:
What is the hyper-cylindrical line element?
You will get better answers if you can tell us a bit more. Where did you come across the term? What parts of the discussion there made sense to you and what parts left you confused? You'll get a bunch of hits if you google for "hypercylindrical line element" - do they help, and if not, what more specific questions do they leave you with?
 
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I am trying to describe sound wave propagation in the real projective space RP3. This procedure has been done for sound wave propagation on a background in a medium with the background topology of RP2 - using a line element with cylindrical coordinates. The FULL cylindrical line element is easily found.. and as shown below in the spacetime metric of an anisotropic uniaxial system in three-dimensions. I am looking for the FULL hyper-cylindrical line element --- and am having a lot of trouble finding it! just looking to see if anyone knows of it.

Signed, Mechanical engineer / Materials Science Phd student striving for a theory..
 

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