Abstract
In this paper, we develop the geometry of bounded Fr\'{e}chet manifolds. We prove that a bounded Fr\'{e}chet tangent bundle admits a vector bundle structure. But, the second order tangent bundle $T^2M$ of a bounded Fr\'{e}chet 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 an integral curve of a vector field on $M$.
Citation
Kaveh Eftekharinasab. "Geometry of bounded Fréchet manifolds." Rocky Mountain J. Math. 46 (3) 895 - 913, 2016. https://doi.org/10.1216/RMJ-2016-46-3-895
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