Tohoku Mathematical Journal
2025
June
SECOND SERIES VOL. 77, NO. 2

Tohoku Math. J.
77 (2025), 269-297

Title FORMAL FRAMES AND DEFORMATIONS OF AFFINE CONNECTIONS

Author Taro Asuke

(Received April 13, 2023, revised June 6, 2023)
Abstract. We will introduce formal frames of manifolds, which are a generalization of ordinary frames. Their fundamental properties are discussed. In particular, canonical forms are introduced, and torsions are defined in terms of them as a generalization of the structural equations. It will be shown that the vanishing of torsions are equivalent to the realizability of given formal frames as ordinary frames. We will also discuss deformations of linear connections on tangent bundles. An application to deformations of foliations are then given.

Mathematics Subject Classification. Primary 53B05; Secondary 58A20, 58H15, 57R32, 57R20.
Key words and phrases. Connections, canonical forms, torsions, deformations.

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