# Coherent Tangent Bundles and Gauss–Bonnet Formulas for Wave Fronts

@article{Saji2009CoherentTB, title={Coherent Tangent Bundles and Gauss–Bonnet Formulas for Wave Fronts}, author={Kentaro Saji and Masaaki Umehara and Kotaro Yamada}, journal={Journal of Geometric Analysis}, year={2009}, volume={22}, pages={383-409} }

We give a definition of ‘coherent tangent bundles’, which is an intrinsic formulation of wave fronts. In our application of coherent tangent bundles for wave fronts, the first fundamental forms and the third fundamental forms are considered as induced metrics of certain homomorphisms between vector bundles. They satisfy the completely same conditions, and so can reverse roles with each other. For a given wave front of a 2-manifold, there are two Gauss–Bonnet formulas. By exchanging the roles of…

## 27 Citations

The Gauss–Bonnet Theorem for Coherent Tangent Bundles over Surfaces with Boundary and Its Applications

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In Saji et al. (J Math 62:259–280, 2008; Ann Math 169:491–529, 2009; J Geom Anal 222):383–409, 2012) the Gauss–Bonnet formulas for coherent tangent bundles over compact-oriented surfaces (without…

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