Open Access
2016 Geometry of bounded Fréchet manifolds
Kaveh Eftekharinasab
Rocky Mountain J. Math. 46(3): 895-913 (2016). DOI: 10.1216/RMJ-2016-46-3-895


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 $M$.


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Kaveh Eftekharinasab. "Geometry of bounded Fréchet manifolds." Rocky Mountain J. Math. 46 (3) 895 - 913, 2016.


Published: 2016
First available in Project Euclid: 7 September 2016

zbMATH: 1359.58004
MathSciNet: MR3544838
Digital Object Identifier: 10.1216/RMJ-2016-46-3-895

Primary: 58A05 , 58B25
Secondary: 37C10

Keywords: Bounded Fréchet manifold , Connection , second order tangent bundle , vector field

Rights: Copyright © 2016 Rocky Mountain Mathematics Consortium

Vol.46 • No. 3 • 2016
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