Geodesic
The mandala of Legendrian dualities for pseudo-spheres in Lorentz-Minkowski space and ``flat'' spacelike surfaces
Journal of Singularities, Tome 2 (2010), pp. 92-127

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Using the Legendrian dualities between surfaces in pseudo-spheres in Lorentz-Minkowski 4-space, we study various kind of flat surfaces in pseudo-spheres. We consider a surface in the pseudo-sphere and its dual surface. Flatness of a surface is defined by the degeneracy of the dual surface similar to the case for the Gauss map of a flat surface in the Euclidean space. We study singularities of these flat surfaces and dualities of singularities.
DOI : 10.5427/jsing.2010.2g
Classification : 53A35, 57R45, 53C42 
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     author = {Shyuichi Izumiya and Kentaro Saji},
     title = {The mandala of {Legendrian} dualities for pseudo-spheres in {Lorentz-Minkowski} space and ``flat'' spacelike surfaces},
     journal = {Journal of Singularities},
     pages = {92--127},
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Shyuichi Izumiya; Kentaro Saji. The mandala of Legendrian dualities for pseudo-spheres in Lorentz-Minkowski space and ``flat'' spacelike surfaces. Journal of Singularities, Tome 2 (2010), pp. 92-127. doi: 10.5427/jsing.2010.2g

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