Abstract
We define generalized null 2-type submanifolds in the m-dimensional Euclidean space 𝔼m. Generalized null 2-type submanifolds are a generalization of null 2-type submanifolds defined by B.-Y. Chen satisfying the condition Δ H = f H + gC for some smooth functions f, g and a constant vector C in 𝔼m, where Δ and H denote the Laplace operator and the mean curvature vector of a submanifold, respectively. We study developable surfaces in 𝔼3 and investigate developable surfaces of generalized null 2-type surfaces. As a result, all cylindrical surfaces are proved to be of generalized null 2-type. Also, we show that planes are the only tangent developable surfaces which are of generalized null 2-type. Finally, we characterize generalized null 2-type conical surfaces.
Acknowledgements
The fourth author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2015R1D1A1A01060046).
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