On Generalized Constant Ratio Surfaces of Higher Codimension

Abstract

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 $${\mathbb {E}}^4$$ . Then, we get complete local classification of CS surfaces in $${\mathbb {E}}^4$$ . We also study GCR surfaces in terms of some of its geometrical invariants.