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Classification of Timelike Constant Slope Surfaces in 3-Dimensional Minkowski Space

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A surface in the Minkowski 3-space is called a constant slope surface if its position vector makes a constant angle with the normal at each point on the surface. In this paper, we give a complete classification of timelike constant slope surfaces in the three dimensional Minkowski space.

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References

  1. Cermelli P., Di Scala A.J.: Constant-angle surfaces in liquid crystals. Philos. Mag. 87, 1871–1888 (2007)

    Article  Google Scholar 

  2. Chen B.Y.: Geometry of Submanifolds. Dekker, New York (1973)

    MATH  Google Scholar 

  3. Dillen F., Fastenakels J., Van der Veken L., Vrancken L.: Constant angle surfaces in \({\mathbb{S}^2\times\mathbb{R}}\) . Monatsh. Math. 152(2), 89–96 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  4. Dillen F., Munteanu M.I.: Constant angle surfaces in \({\mathbb{H}^2\times\mathbb{R}}\) . Bull. Braz. Math. Soc. 40(1), 1–13 (2009)

    Article  MathSciNet  Google Scholar 

  5. Fastenakels J., Munteanu M.I., Van der Veken J.: Constant angle surfaces in the Heisenberg group. Acta Math. Sin. (Engl. Ser.) 27(4), 747–756 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  6. Fu Y., Yang D.: On constant slope spacelike surfaces in 3-dimensional Minkowski space. J. Math. Anal. Appl. 385(1), 208–220 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  7. Hano J., Nomizu K.: Surfaces of revolution with constant mean curvature in Lorentz-Minkowski space. Tohoku Math. J. (2) 32(3), 427–437 (1984)

    Article  MathSciNet  Google Scholar 

  8. López R., Munteanu M.I.: Constant angle surfaces in Minkowski space. Bull. Belg. Math. Soc. Simon Stevin. 18(2), 271–286 (2011)

    MathSciNet  MATH  Google Scholar 

  9. Munteanu M.I.: From golden spirals to constant slope surfaces. J. Math. Phys. 51, 073507 (2010)

    Article  MathSciNet  Google Scholar 

  10. Munteanu M.I., Nistor A.I.: A new approach on constant angle surfaces in \({\mathbb{E}^3}\) . Turkish J. Math. 33(1), 1–10 (2009)

    MathSciNet  Google Scholar 

  11. O’Neill B.: Semi-Riemannian Geometry with Applications to Relativity. Academic Press, New York (1982)

    Google Scholar 

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Correspondence to Yu Fu.

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Fu, Y., Wang, X. Classification of Timelike Constant Slope Surfaces in 3-Dimensional Minkowski Space. Results. Math. 63, 1095–1108 (2013). https://doi.org/10.1007/s00025-012-0255-9

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  • DOI: https://doi.org/10.1007/s00025-012-0255-9

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