The Taylor Expansion of the Exponential Map and Geometric Applications
Abstract
In this work we consider the Taylor expansion of the exponential map of a submanifold immersed in Rn 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 R3. Also we compute, by using the Taylor expansion, the directions of high contact with hyperspheres of a surface immersed in R4 and the asymptotic directions of a surface immersed in R5.
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