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90,530
The Geometry of the Frame Bundle over Spacetime
, 2008
"... One of the known mathematical descriptions of singularities in General Relativity is the bboundary, which is a way of attaching endpoints to inextendible endless curves in a spacetime. The bboundary of a manifold M with connection Γ is constructed by forming the Cauchy completion of the frame bund ..."
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One of the known mathematical descriptions of singularities in General Relativity is the bboundary, which is a way of attaching endpoints to inextendible endless curves in a spacetime. The bboundary of a manifold M with connection Γ is constructed by forming the Cauchy completion of the frame
Stochastic Cohomology of the Frame Bundle of the Loop Space
, 1997
"... We study the differential forms over the frame bundle of the based loop space. They are stochastics in the sense that we put over this frame bundle a probability measure. In order to understand the curvatures phenomena which appear when we look at the Lie bracket of two horizontal vector fields, we ..."
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We study the differential forms over the frame bundle of the based loop space. They are stochastics in the sense that we put over this frame bundle a probability measure. In order to understand the curvatures phenomena which appear when we look at the Lie bracket of two horizontal vector fields, we
Stochastic Cohomology of the Frame Bundle of the Loop Space
, 1997
"... We study the differential forms over the frame bundle of the based loop space. They are stochastics in the sense that we put over this frame bundle a probability measure. In order to understand the curvatures phenomena which appear when we look at the Lie bracket of two horizontal vector fields, we ..."
Abstract
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We study the differential forms over the frame bundle of the based loop space. They are stochastics in the sense that we put over this frame bundle a probability measure. In order to understand the curvatures phenomena which appear when we look at the Lie bracket of two horizontal vector fields, we
INVARIANCE OF gNATURAL METRICS ON LINEAR FRAME BUNDLES
"... Abstract. In this paper we prove that each gnatural metric on a linear frame bundle LM over a Riemannian manifold (M, g) is invariant with respect to a lifted map of a (local) isometry of the base manifold. Then we define gnatural metrics on the orthonormal frame bundle OM and we prove the same in ..."
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Abstract. In this paper we prove that each gnatural metric on a linear frame bundle LM over a Riemannian manifold (M, g) is invariant with respect to a lifted map of a (local) isometry of the base manifold. Then we define gnatural metrics on the orthonormal frame bundle OM and we prove the same
Geodesic Reduction via Frame Bundle Geometry
"... Abstract. A manifold with an arbitrary affine connection is considered and the geodesic spray associated with the connection is studied in the presence of a Lie group action. In particular, results are obtained that provide insight into the structure of the reduced dynamics associated with the given ..."
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Cited by 2 (0 self)
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with the given invariant affine connection. The geometry of the frame bundle of the given manifold is used to provide an intrinsic description of the geodesic spray. A fundamental relationship between the geodesic spray, the tangent lift and the vertical lift of the symmetric product is obtained, which provides
ON CURVATURES OF LINEAR FRAME BUNDLES WITH NATURALLY LIFTED METRICS
"... Abstract. We study some simple natural metrics on the linear frame bundle L M over a Riemannian manifold (M, g) which generalize the socalled diagonal metric introduced by K. P. Mok in 1978. We derive the basic formulas for the LeviCivita connection and the curvature tensor. Next, we limit ourselv ..."
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Abstract. We study some simple natural metrics on the linear frame bundle L M over a Riemannian manifold (M, g) which generalize the socalled diagonal metric introduced by K. P. Mok in 1978. We derive the basic formulas for the LeviCivita connection and the curvature tensor. Next, we limit
A Frame Bundle Generalization of Multisymplectic Momentum Mappings ∗†
, 2001
"... This paper presents generalized momentum mappings for covariant Hamiltonian field theories. The new momentum mappings arise from a generalization of symplectic geometry to LV Y, the bundle of vertically adapted linear frames over the bundle of field configurations Y. Specifically, the generalized fi ..."
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Cited by 1 (1 self)
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This paper presents generalized momentum mappings for covariant Hamiltonian field theories. The new momentum mappings arise from a generalization of symplectic geometry to LV Y, the bundle of vertically adapted linear frames over the bundle of field configurations Y. Specifically, the generalized
Results 1  10
of
90,530