I am looking for some reading material that would encompass tensor algebra on complex hermitian spaces (not necessarily complex manifolds). Of course I looked in every tensor algebra course I could put my hands on, but complex spaces are never discussed.
What I could find was complex differential geometry, kahler manifolds and such, but it's way too far off... I'm only interested in the basic definitions of tensors (covariant/contravariant components, metric tensor, etc.) over complex spaces and especially how complex conjugation is treated. Thanks
I'm reading Modern Geometry — Methods and Applications Part I. The Geometry of Surfaces, Transformation Groups, and Fields by B. A. DubrovinA. T. FomenkoS. P. Novikov
https://link.springer.com/book/10.1007%2F978-1-4684-9946-9
The section 11 and section 27 treat the case complexe, though I have also some doubts in this materiel. We can discuss if you like.