Cuspidal edges and swallowtails are typical non-degenerate singular points on wave fronts in the Euclidean -space. Their first fundamental forms belong to a class of positive semi-definite metrics called "Kossowski metrics". A point where a Kossowski metric is not positive definite is called a singular point or a se…
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4 results for “Kossowski”
In this paper, we give two classes of positive semi-definite metrics on 2-manifolds. The one is called a class of Kossowski metrics and the other is called a class of Whitney metrics: The pull-back metrics of wave fronts which admit only cuspidal edges and swallowtails in are Kossowski metrics, and t…
Develops a new family of signature-changing models on metric manifolds.
problem Signature changes in metric manifolds.
method One-parameter family of Lorentz-Riemann models, local expressions around change.
result Generalizes existing signature-changing models.
In a previous work, the authors introduced the notion of `coherent tangent bundle', which is useful for giving a treatment of singularities of smooth maps without ambient spaces. Two different types of Gauss-Bonnet formulas on coherent tangent bundles on 22-dimensional manifolds were proven, and several applications to…