6533b7cefe1ef96bd1256f4b
RESEARCH PRODUCT
The geometry of corank 1 surfaces in ℝ4
R. Oset SinhaP. Benedini RiulMaria Aparecida Soares Ruassubject
General MathematicsGeometryMathematics::Differential GeometryMathematicsdescription
Abstract We study the geometry of surfaces in ℝ4 with corank 1 singularities. For such surfaces, the singularities are isolated and, at each point, we define the curvature parabola in the normal space. This curve codifies all the second-order information of the surface. Also, using this curve, we define asymptotic and binormal directions, the umbilic curvature and study the flat geometry of the surface. It is shown that we can associate to this singular surface a regular one in ℝ4 and relate their geometry.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-12-21 | The Quarterly Journal of Mathematics |