Self Similar Surfaces in Euclidean Spaces

Kadri Arslan, Esra Etemoğlu, Betül Bulca

Abstract


In the present study we consider self-similar surfaces imbedded in Euclidean space. We give necessary and sufficient conditions for the surface ofrevolution and surfaces with Monge patch in \(E^{3}\) to become self-similar. Further, we investigate self-similar surfaces in Euclidean 4-space \(E^{4}\):

Additionally we give necessary and sufficient condition of spherical product surfaces and smooth surfaces given with the Monge patch in \(E^{4}\) to become self-similar.


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