surfing the internet to look for good books and have stumbled on this one, just scanning few pages i can already say this is a good book, may come handy for pre-requisite refresher topics
Introduction to Differential Geometry
https://link.springer.com/book/10.1007/978-3-662-64340-2

(just posting today, an mwfsat day, what has been done yesterday, a tthsun day), here, adhering to what is analogous to Kaluza's cylinder hypothesis
https://foxtrotpaparomeo.wordpress.com/2023/01/11/11012023rough-draftstatic-solutions-to-einsteins-field-equations-in-11-space-time/