Differential Geometry of Microlinear Frolicher Spaces I

Details Differential Geometry of Microlinear Frolicher Spaces I Differential Geometry of Microlinear Frolicher Spaces I

2010-02-22

arxiv.org/abs/1002.3978v3

Mathematics

Differential Geometry

Scientific paper

The central object of synthetic differential geometry is microlinear spaces. In our previous paper [Microlinearity in Frolicher spaces -beyond the regnant philosophy of manifolds-, International Journal of Pure and Applied Mathematics, 60 (2010), 15-24] we have emancipated microlinearity from within well-adapted models to Frolicher spaces. Therein we have shown that Frolicher spaces which are microlinear as well as Weil exponentiable form a cartesian closed category. To make sure that such Frolicher spaces are the central object of infinite-dimensional differential geometry, we develop the theory of vector fields on them in this paper. The central result is that all vector fields on such a Frolicher space form a Lie algebra.

Affiliated with

Also associated with

No associations

Rating

Differential Geometry of Microlinear Frolicher Spaces I does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Differential Geometry of Microlinear Frolicher Spaces I, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Differential Geometry of Microlinear Frolicher Spaces I will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-372733