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arXiv · 1303.1128

Geometry of Bounded Frechet Manifolds

Kaveh Eftekharinasab
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Abstract

In this paper we develop the geometry of bounded Fr\'echet manifolds. We prove that a bounded Fr\'echet tangent bundle admits a vector bundle structure. But the second order tangent bundle $T^2M$ of a bounded Fr\'echet manifold $M$, becomes a vector bundle over $M$ if and only if $M$ is endowed with a linear connection. As an application, we prove the existence and uniqueness of the integral curve of a vector field on $M$.

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Kaveh Eftekharinasab. 2013-03-05. Geometry of Bounded Frechet Manifolds. https://doi.org/10.1216/rmj-2016-46-3-895

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