arXiv subjects

A. Montesinos-Amilibia

Publications and source records attributed to A. Montesinos-Amilibia.

2 recordsLinked to original sources

arXiv2012

The Taylor Expansion of the Exponential Map and Geometric Applications

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.

math.DG↗

arXiv1999

The self-linking number of a closed curve in R^n

We introduce the self-linking number of a smooth closed curve in R^n with respect to a 3-dimensional vector bundle over the curve, provided that some regularity conditions are satisfied. When n=3, this construction gives the classical self-linking number of a closed embedded curve with non-vanishing curvature. We also look at some interesting particular cases, which correspond to the osculating or the orthogonal vector bundle of the curve.

math.DG↗