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“…Recently, we study the non-transversal intersection of parametric-parametric-parametric (PPP) hypersurfaces [19] and the non-transversal intersection of implicit-implicit-parametric (IIP), implicit-parametric-parametric (IPP) hypersurfaces [20] in E 4 (we review the previous studies given for intersection problems in these publications).…”

confidence: 99%

“…Recently, we study the non-transversal intersection of parametric-parametric-parametric (PPP) hypersurfaces [19] and the non-transversal intersection of implicit-implicit-parametric (IIP), implicit-parametric-parametric (IPP) hypersurfaces [20] in E 4 (we review the previous studies given for intersection problems in these publications).…”

confidence: 99%

“…Since surfaces can also be defined by their implicit equations, differential geometry of the intersection curve of two implicit surfaces has been studied in E 3 by [2,12,20,21] and of three implicit hypersurfaces has been studied in E 4 by [3,4,7,14,19]. There also exist some studies for the intersection curves of different type surfaces in E 3 [10,18,21] and in E 4 [1,8,10,14]. On the other hand, by using the wedge product of two vectors in (n + 1)-dimensions, Goldman [12] derived a closed formula for the first curvature of the transversal intersection of n-implicit hypersurfaces in (n + 1)-dimensions.…”

confidence: 99%

“…A general reference including many topics in semi-Riemannian geometry is the classical book [19]. Differential geometry of the intersection curves in R 3 and R 4 can be found in [14,26,23,1,15,7,2,4,8,5,3].…”

confidence: 99%