I know this may sound quite as an old adagio, but I have some problems, or at least some concerns, about some chapter title in D'Inverno GR textbook. I'm referring to the chapter devoted to Tensor Algebra:(adsbygoogle = window.adsbygoogle || []).push({});

Within them you can find definitions like:

- Contravariant tensors
- Covariant and mixed tensors

"A contravariant vector or contravariant tensor of rank (order) 1 is a set of quantities, written..."

similarly for the "covariant tensors".

This is really a painful definition to me, since I've learnt the tensors areinvariant objects, i.e. are neither covariant nor contravariant. You can of course get the tensors component related to some basis, but this is a different story. I mean, you can take a vector and expressing it as the linear combination of the basis vectors (coordinate basis) through the contravariant component of it. But nothing prevent us to express the same vector as a linear combination of covariant components, referred to some 1-form basis.

All in all, you can always raise or lower indices using the metric, but these are the components, not the tensorper se. I find quite misleading confusing the object itself with its contravariant/covariant/mixed components...

An I right in claiming this? (It's not of course about judging the D'Inverno textbook, which is one of the many GR superb books I have in my collection, but to confirm/confute my understanding about this topic).

Recently I've also looked throughGouge field, knots and gravityby Baez once more (every time I run through it, I discover new ways of reading the chapters, that's incredible to me) and I see it's presentation less confusing, since classifies vectors and 1-forms by they way they are pulled back or push, forward.

What you think about this?

Thanks for your support.

Ricky

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# I Misleading naming in D'Inverno textbook

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**