Geodesic
On Projective Umbilics: a Geometric Invariant and an Index
Journal of Singularities, Tome 17 (2018), pp. 81-90

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We define a geometric invariant and an index (+1 or -1) for projective umbilics of smooth surfaces. We prove that the sum of the indices of the projective umbilics inside a connected component H of the hyperbolic domain remains constant in any 1-parameter family of surfaces if the topological type of H does not change. We prove the same statement for any connected component E of the elliptic domain. We give formulas for the invariant and for the index which do not depend on any normal form.
DOI : 10.5427/jsing.2018.17e
Classification : 53A20, 53A55, 53D10, 57R45, 58K05 
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     author = {Ricardo Uribe-Vargas},
     title = {On {Projective} {Umbilics:} a {Geometric} {Invariant} and an {Index}},
     journal = {Journal of Singularities},
     pages = {81--90},
     publisher = {mathdoc},
     volume = {17},
     year = {2018},
     doi = {10.5427/jsing.2018.17e},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2018.17e/}
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Ricardo Uribe-Vargas. On Projective Umbilics: a Geometric Invariant and an Index. Journal of Singularities, Tome 17 (2018), pp. 81-90. doi: 10.5427/jsing.2018.17e

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