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Abstract
We consider a class $ \mathcal{Q}(M) \,$ consisting of smooth
quartic differential forms which are defined on an oriented
two-manifold $ M $, to each of which we associate a pair of
transversal nets with common singularities. These quartic forms are
related to geometric objects such as curvature lines, asymptotic
lines of surfaces immersed in $\R^4.$ Local problems around the
rank-2 singular points of the elements of $ \mathcal{Q}(M) \,$,
such as stability, normal forms, finite determinacy, versal
unfoldings, are studied in [2]. Here we make a similar study
for a rank-1 singular point that is analogous to the saddle-node
singularity of vector fields.
Mathematics Subject Classification: Primary: 53A07, 58D10; Secondary: 37G10.
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