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Homothetical Surfaces in Three Dimensional Pseudo–Galilean Spaces Satisfying \(\Delta ^{II}\mathbf{x }_i=\lambda _i\mathbf{x }_i\)

  • Mohamd Saleem LoneEmail author
Article
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Abstract

A homothetical surface arises as a graph of a function \(z = \varphi _1(v_1) \varphi _2(v_2)\). In this paper, we study the homothetical surfaces in three dimensional pseudo-Galilean space\(\left( \mathbb {G}_3^1\right) \) satisfying the conditions \(\Delta ^{II}\mathbf{x }_i=\lambda _i\mathbf{x }_i,\) where \(\Delta ^{II}\) is the Laplacian with respect to second fundamental form. In particular, we show the non-existence of any such type of surface in \(\mathbb {G}_3^1.\)

Keywords

Homothetical surface Finite type surface Laplacian operator Pseudo-Galilean space 

Mathematics Subject Classification

Primary 53A35 Secondary 53B30 53A40 

Notes

Acknowledgements

I am very thankful to the anonymous referees for their valuable comments and suggestions which helped a lot to improve the quality of this paper.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.International Centre for Theoretical SciencesTata Institute of Fundamental ResearchBengaluruIndia

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