On frames defined by horizontal spaces

León, Manuel de; Ortaçgil, Ercüment H.

doi:10.21136/cmj.1996.127287

Cited by 4 publications

(1 citation statement)

References 3 publications

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“…is the prolonged map of a local diffeomorphism F : M 1 → M 2 between the corresponding linear frame bundles. In order to describe second order frames in local coordinates [7,11], we put φ(r a ) ≡ (φ i (r a ), φ i j (r a )), where {r a } are the natural coordinates in R n . Then the nonholonomic frame j 1 0 φ is expressed as…”

Section: Preliminarsmentioning

confidence: 99%

Principal bundle structures among second order frame bundles

León¹,

Méndez²

2015

Preprint

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Using a model for the bundle F 2 M of semi-holonomic second order frames of a manifold M as an extension of the bundle F 2 M of holonomic second order frames of M , we introduce in F 2 M a principal bundle structure over F 2 M , the structure group being the additive group A 2 (n) of skew-symmetric bilinear maps from R 2 × R n into R n . The composition of the projection of that structure with the existing projection of the bundle F 2 M of non-holonomic second order frames of M over F 2 M provides a principal bundle structure in F 2 M over F 2 M . These results close an existing gap in the theory of second order frame bundles.

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Section: Preliminarsmentioning

confidence: 99%

Principal bundle structures among second order frame bundles

León¹,

Méndez²

2015

Preprint

View full text Add to dashboard Cite

show abstract

Principal bundle structures among second order frame bundles

León¹,

Méndez²

2016

Differential Geometry and its Applications

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Abstract. Using a model for the bundleF 2 M of semi-holonomic second order frames of a manifold M as an extension of the bundle F 2 M of holonomic second order frames of M , we introduce inF 2 M a principal bundle structure over F 2 M , the structure group being the additive group A 2 (n) of skew-symmetric bilinear maps from R 2 × R n into R n . The composition of the projection of that structure with the existing projection of the bundleF 2 M of non-holonomic second order frames of M overF 2 M provides a principal bundle structure inF 2 M over F 2 M . These results close an existing gap in the theory of second order frame bundles.

show abstract