On generalized constant ratio surfaces with higher codimension

TL;DR

This paper investigates generalized constant ratio surfaces in four-dimensional Euclidean space and classifies constant slope surfaces, expanding understanding of their geometric properties and classifications.

Contribution

It provides a classification of constant slope surfaces and explores generalized constant ratio surfaces in Euclidean 4-space, offering new insights into their structure.

Findings

Classification of constant slope surfaces

Characterization of generalized constant ratio surfaces

Extension of geometric properties to higher dimensions

Abstract

In this paper, we study generalized constant ratio surfaces in the Euclidean 4-space. We also obtain a classifications of constant slope surfaces.