Book on tensor symmetry, geometries, surfaces

[desA]

I'm looking for a good tensor reference book that provides insights into the following areas of tensors:

1. Symmetries & how to extract them.

2. Full tensor visualisation eg. how to visualise the stress tensor in its 9 component form without resorting to a split into 3 simultaneous equations.

3. Geometric interpretations of tensors.

I am researching into the Navier-stokes equations from a physical, fluids background & would like to further explore along tensor lines.

Thanks so much for your assistance.

desA

 

[Chris Hillman]

Hi, desA,

I don't know of a single book which will fill all your requirements, but it might help to know that you can probably pick up some knowledge of the invariants of tensors from good books on classical invariant theory and on representation theory. For visual intuition regarding tensors and exterior forms, you can try Burke, Applied Differential Geometry.

Hope this helps,

Chris Hillman

 

[desA]

Thanks very much for your useful information, Chris. I've been working through a number of the classical tensor books & have some new insights. I'll look into Burke & see where that leads me. Thanks again.

desA