Rocky Mountain Journal of Mathematics

Geometry of bounded Fréchet manifolds

Kaveh Eftekharinasab

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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 $M$.

Article information

Source
Rocky Mountain J. Math., Volume 46, Number 3 (2016), 895-913.

Dates
First available in Project Euclid: 7 September 2016

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1473275765

Digital Object Identifier
doi:10.1216/RMJ-2016-46-3-895

Mathematical Reviews number (MathSciNet)
MR3544838

Zentralblatt MATH identifier
1359.58004

Subjects
Primary: 58A05: Differentiable manifolds, foundations 58B25: Group structures and generalizations on infinite-dimensional manifolds [See also 22E65, 58D05]
Secondary: 37C10: Vector fields, flows, ordinary differential equations

Keywords
Bounded Fréchet manifold second order tangent bundle connection vector field

Citation

Eftekharinasab, Kaveh. Geometry of bounded Fréchet manifolds. Rocky Mountain J. Math. 46 (2016), no. 3, 895--913. doi:10.1216/RMJ-2016-46-3-895. https://projecteuclid.org/euclid.rmjm/1473275765


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