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Conjugate connections and dierential equations on innite dimensional manifolds
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The article was published on 2006-01-01 and is currently open access. It has received 6 citations till now. The article focuses on the topics: Normal bundle & Unit tangent bundle.read more
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Some recent work in Frechet geometry
TL;DR: In this article, an earlier result on the structure of second tangent bundles in the finite dimensional case was extended to infinite dimensional Banach manifolds and Frechet manifolds that could be represented as projective limits of Banach manifold.
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Second order structures for sprays and connections on Frechet manifolds
TL;DR: In this article, it is proved that the existence of Christoel and Hessian structures, connections, sprays and dissections are equivalent on those Fr echet manifolds which can be considered as projective limits of Banach manifolds.
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Projective and Direct limits of Banach $G$ and tensor structures
P. Cabau,F. Pelletier +1 more
TL;DR: In this article, the limits of Banach tensor structures with Frechet structures and adapted connections to $G$-structures in both frameworks are studied. But the authors focus on the case where the connection between the two structures is not projective.
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Geometric structure for the tangent bundles of direct limit manifolds
TL;DR: In this paper, the direct limit of tangent bundles of paracompact finite dimensional manifolds with a structure of convenient vector bundle with structural group GL(∞,R) = lim→ GL(R n ).
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Projective limits of local shift morphism
TL;DR: In this article, the authors define the notion of projective limit of local shift morphisms and endow the space of such mathematical objects with an adapted differential structure, and illustrate this notion with the famous KdV equation on the circle, for which one can associate a couple of compatible Poisson tensors of this type on the Hilbert tower
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A general theory of quantum relativity
Djordje Minic,Chia-Hsiung Tze +1 more
TL;DR: In this article, the authors propose a background independent quantum theory of gravity and matter based on the interplay between the symplectic form, dynamical metric and non-integrable almost complex structure of the space of quantum events.
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Isoperimetric Conditions, Poisson Problems, and Diffusions in Riemannian Manifolds
TL;DR: In this paper, the authors studied the exit time moments of natural diffusions from smoothly bounded domains in a complete Riemannian manifold with compact closure, and proved an analog of the Faber-Krahn theorem.