Abstract
In the late 1990s, B. Y. Chen introduced the notion of special slant surfaces in Kähler surfaces and classified non-minimal proper special slant surfaces with constant mean curvature in 2-dimensional complex space forms. In this paper, we completely classify proper special slant surfaces with non-constant mean curvature in 2-dimensional complex space forms.
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References
Castro, I.: Lagrangian surfaces with circular ellipse of curvature in complex space forms. Math. Proc. Cambridge Philos. Soc. 136, 239–245 (2004)
Chen, B.Y.: Geometry of Slant Submanifolds. Katholieke Universiteit Leuven, Belgium (1990)
Chen, B.Y.: Jacobi’s elliptic functions and Lagrangian immersions. Proc. Roy. Soc. Edinburgh Sec. A 126, 687–704 (1996)
Chen, B.Y.: Intrinsic and extrinsic structures of Lagrangian surfaces in complex space forms. Tsukuba J. Math. 22, 657–680 (1998)
Chen, B.Y.: Special slant surfaces and a basic inequality. Result. Math. 33, 63–78 (1998)
Chen, B.Y.: On slant surfaces. Taiwanese J. Math. 3, 163–179 (1999)
Chen, B.Y.: Classification of slumbilical submanifolds in complex space forms. Osaka J. Math. 39, 23–47 (2002)
Chen, B.Y.: On purely real surfaces in Kaehler surfaces. Turk. J. Math. 34, 275–292 (2010)
Chen, B.Y., Tazawa, Y.: Slant submanifolds of complex projective and complex hyperbolic spaces. Glasgow Math. J. 42, 439–454 (2000)
Chen, B.Y., Vrancken, L.: Lagrangian submanifolds satisfying a basic equality. Math. Proc. Cambridge Philos. Soc. 120, 291–307 (1996)
Chen, B.Y., Vrancken, L.: Existence and Uniqueness Theorem for slant immersions and applications. Result. Math. 31, 28–39 (1997)
Chen, B.Y., Vrancken, L.: Addendum to: Existence and Uniqueness Theorem for slant immersions and applications. Result. Math. 39, 18–22 (2001)
Chen, B.Y., Vrancken, L.: Slant surfaces with prescribed Gaussian curvature. Balkan J. Geom. Appl. 7, 29–36 (2002)
Hirakawa, S.: Constant Gaussian curvature surfaces with parallel mean curvature vector in two-dimensional complex space forms. Geom. Dedic. 118, 229–244 (2006)
Kenmotsu, K.: Classification of surfaces with parallel mean curvature vector in two-dimensional complex space forms. Amer. J. Math. 122, 295–317 (2000)
Kenmotsu, K.: Complete parallel mean curvature surfaces in two-dimensional complex space forms. Bull. Braz. Math. Soc. 49, 775–788 (2018)
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Sasahara, T. Special Slant Surfaces with Non-constant Mean Curvature in 2-Dimensional Complex Space Forms. Results Math 77, 180 (2022). https://doi.org/10.1007/s00025-022-01712-6
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DOI: https://doi.org/10.1007/s00025-022-01712-6