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arXiv · 1210.5971

The Taylor Expansion of the Exponential Map and Geometric Applications

M. G. Monera·A. Montesinos-Amilibia·E. Sanabria-Codesal
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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.

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M. G. Monera, A. Montesinos-Amilibia, E. Sanabria-Codesal. 2012-10-22. The Taylor Expansion of the Exponential Map and Geometric Applications. https://arxiv.org/abs/1210.5971

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