Is there a book (or a few books) that gives the basic theory of the different types of manifolds and their geometries in an integrated manner? By the different types I primary mean C^k real manifolds, complex manifolds, real analytic and non-archimeadian (p-adic).
2026-04-08 13:10:02.1775653802
A book that includes the main types of manifolds and geometries
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As far as I know, the p-adic case is never discussed in conjunction with the "standard" geometric structures. Most people who care about p-adic structures come from the algebraic geometry side and they do not care about, say, conformal structures or contact structures or foliations on manifolds. If you want the basic theory of geometric structures on $C^\infty$-manifolds, consider reading
Shoshichi Kobayashi , "Transformation Groups in Differential Geometry", (Classics in Mathematics) 1995th Edition, Springer Verlag.
Kobayashi's main interest is in automorphism groups of structures (more precisely, when are they Lie groups), but he also discusses geometric structures in great detail.