On sprays and connections

Kozma, László

Displaying similar documents to “On sprays and connections”

On connections, geodesics and sprays in synthetic differential geometry

Marta Bunge, Patrice Sawyer (1984)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

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On connections on the second iterated tangent bundle

Anton Dekrét (1987)

Archivum Mathematicum

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From the Fermi-Walker to the Cartan connection

Lafuente, Javier, Salvador, Beatriz

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Let $M$ be a $C^{\infty}$ -manifold with a Riemannian conformal structure $C$ . Given a regular curve $γ$ on $M$ , the authors define a linear operator on the space of (differentiable) vector fields along $γ$ , only depending on $C$ , called the Fermi-Walker connection along $γ$ . Then, the authors introduce the concept of Fermi-Walker parallel vector field along $γ$ , proving that such vector fields set up a linear space isomorphic to the tangent space at a point of $γ$ . This allows to consider the Fermi-Walker horizontal...

Higher order Cartan connections

Juraj Virsik (1996)

Archivum Mathematicum

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A Cartan connection associated with a pair $P (M, G^{'}) \subset P (M, G)$ is defined in the usual manner except that only the injectivity of $ω : T (P^{'}) \to T {(G)}_{e}$ is required. For an $r$ -th order connection associated with a bundle morphism $Φ : P^{'} \to P$ the concept of Cartan order $q \leq r$ is defined, which for $q = r = 1, Φ : P^{'} \subset P$ , and $dim M = dim G / G^{'}$ coincides with the classical definition. Results are obtained concerning the Cartan order of $r$ -th order connections that are the product of $r$ first order (Cartan) connections.