Proceedings of the International Conference on Geometry, Integrability and Quantization

Meridian Surfaces of Parabolic Type in the Four-Dimensional Minkowski Space

Georgi Ganchev and Velichka Milousheva

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Abstract

We construct a special class of spacelike surfaces in the Minkowski 4-space which are one-parameter systems of meridians of the rotational hypersurface with lightlike axis and call these surfaces meridian surfaces of parabolic type. They are analogous to the meridian surfaces of elliptic or hyperbolic type. Using the invariants of these surfaces we give the complete classification of the meridian surfaces of parabolic type with constant Gauss curvature or constant mean curvature. We also classify the Chen meridian surfaces of parabolic type and the meridian surfaces of parabolic type with parallel normal bundle.

Article information

Source
Proceedings of the Seventeenth International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov, Guowu Meng and Akira Yoshioka, eds. (Sofia: Avangard Prima, 2016), 243-255

Dates
First available in Project Euclid: 15 December 2015

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1450194160

Digital Object Identifier
doi:10.7546/giq-17-2016-243-255

Mathematical Reviews number (MathSciNet)
MR3445433

Zentralblatt MATH identifier
1345.53020

Citation

Ganchev, Georgi; Milousheva, Velichka. Meridian Surfaces of Parabolic Type in the Four-Dimensional Minkowski Space. Proceedings of the Seventeenth International Conference on Geometry, Integrability and Quantization, 243--255, Avangard Prima, Sofia, Bulgaria, 2016. doi:10.7546/giq-17-2016-243-255. https://projecteuclid.org/euclid.pgiq/1450194160


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