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Connections on higher order principal prolongations

Vašík, Petr (2006)

Proceedings of the 25th Winter School "Geometry and Physics"

Geometric constructions of connections on the higher order principal prolongations of a principal bundle are considered. Moreover, the existing differences among connections on non-holonomic, semiholonomic and holonomic principal prolongations are discussed.

Connections with prescribed curvature

Dennis Deturck, Janet Talvacchia (1987)

Annales de l'institut Fourier

We discuss the problem of prescribing the curvature of a connection on a principal bundle whose base manifold is three-dimensional. In particular, we consider the local question: Given a curvature form F , when does there exist locally a connection A such that F is the curvature of A  ? When the structure group of the bundle is semisimple, a finite number of nonlinear identities arise as necessary conditions for local solvability of the curvature equation. We conjecture that these conditions are also...

Connessioni adattate ad un Riferimento in Relatività Generale

Giorgio Ferrarese, Donato Bini, Gianluca Gemelli (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

I vari metodi di definire connessioni adattate ad un Riferimento fisico vengono qui ricondotti ad un unico formalismo. Viene inoltre introdotta la nozione generale di campo gravitazionale affine adattato (sia al Riferimento che alla connessione).

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