## Rocky Mountain Journal of Mathematics

### Geometry of bounded Fréchet manifolds

Kaveh Eftekharinasab

#### 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

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

#### 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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