The Taylor Expansion of the Exponential Map and Geometric Applications
Differential Geometry
2012-10-23 v1
Abstract
In this work we consider the Taylor expansion of the exponential map of a submanifold immersed in R^n up to order three, in order to introduce the concepts of lateral and frontal deviation. We compute the directions of extreme lateral and frontal deviation for surfaces in R^3. Also we compute, by using the Taylor expansion, the directions of high contact with hyperspheres of a surface immersed in R^4 and the asymptotic directions of a surface immersed in R^5.
Keywords
Cite
@article{arxiv.1210.5971,
title = {The Taylor Expansion of the Exponential Map and Geometric Applications},
author = {M. G. Monera and A. Montesinos-Amilibia and E. Sanabria-Codesal},
journal= {arXiv preprint arXiv:1210.5971},
year = {2012}
}