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2014•International Journal of MathematicsRequires access

CANONICAL FORM IN SECOND-ORDER FRAME BUNDLES IN A NATURAL WAY

Abel Méndez

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Abstract

Using horizontal n-bases of the tangent bundle of the linear frame bundle [Formula: see text] of an n-dimensional manifold M, the canonical form in the non-holonomic second-order frame bundle of M is introduced as a restriction of the canonical form of the bundle [Formula: see text]. This construction generalizes the ones in the corresponding semi-holonomic and holonomic second-order frame bundles. We prove that the natural projection of the set of all non-holonomic second-order frames of M into [Formula: see text] defines a principal bundle structure.

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What this paper is about

Using horizontal n-bases of the tangent bundle of the linear frame bundle [Formula: see text] of an n-dimensional manifold M, the canonical form in the non-holonomic second-order frame bundle of M is introduced as a restriction of the canonical form of the bundle [Formula: see text]. This construction generalizes the ones in the corresponding semi-holonomic and holonomic second-order frame bundles. We prove that the natural projection of the set of all non-holonomic second-order frames of M into [Formula: see text] defines a principal bundle structure.

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Available abstract

Using horizontal n-bases of the tangent bundle of the linear frame bundle [Formula: see text] of an n-dimensional manifold M, the canonical form in the non-holonomic second-order frame bundle of M is introduced as a restriction of the canonical form of the bundle [Formula: see text]. This construction generalizes the ones in the corresponding semi-holonomic and holonomic second-order frame bundles. We prove that the natural projection of the set of all non-holonomic second-order frames of M into [Formula: see text] defines a principal bundle structure.

Key concepts: Mathematics, Frame bundle, Tangent bundle, Holonomic, Principal bundle, Normal bundle, Cotangent bundle, Canonical bundle

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