On Generalized Constant Ratio Surfaces of Higher Codimension - Kelleci, Alev; Turgay, Nurettin Cenk; Erguet, Mahmut (Springer Basel Ag, 2019)
In this paper, we introduce constant slope (CS) and generalized constant ratio (GCR) submanifolds with higher codimension in Euclidean spaces. We firstly obtain a classification of GCR surfaces in Euclidean 4-spaces E4. Then, we get complete local classification of CS surfaces in E4. We also study GCR surfaces in terms of some of its geometrical invariants.
Keywords: Euclidean spaces; generalized constant ratio submanifolds; constant slope surfaces; position vector; canonical principal direction