Certain classifications on quadrics in simply isotropic space $ \mathbb{I}^{3} $

Hamza Alzaareer; Hassan Al-Zoubi; Farhan Abdel-Fattah; Hamza Alzaareer; Hassan Al-Zoubi; Farhan Abdel-Fattah

doi:10.3934/math.20251172

AIMS Mathematics

2025, Volume 10, Issue 11: 26662-26679. doi: 10.3934/math.20251172

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Research article

Certain classifications on quadrics in simply isotropic space $ \mathbb{I}^{3} $

1.
Department of Mathematics, Al-Zaytoonah University of Jordan, P.O. Box 130, Amman, Jordan, 11733; Email: h.alzaareer@zuj.edu.jo
2.
Department of Cyber Security, Al-Zaytoonah University of Jordan, P.O. Box 130, Amman, Jordan, 11733; Email: Farahan.A@zuj.edu.jo

Received: 21 July 2025 Revised: 13 October 2025 Accepted: 06 November 2025 Published: 18 November 2025
MSC : 53A40, 53A35, 53B25

In this paper, we deal with the natural geometry of quadric surfaces in the isotropic space $ \mathbb{I}^{3} $. We provided defining equations for the $ 3^{rd}, 4^{th} $ type ruled surfaces and $ 1^{st}, 2^{nd} $ type of quadric surfaces. In this paper, we investigated the finite Chen-type of ruled and quadric surfaces in the 3-dimensional simply isotropic space $ \mathbb{I}^{3} $, corresponding to the third fundamental form of the surface.
- surfaces in the simply isotropic 3-space,
- surfaces of finite Chen-type,
- Beltrami operator,
- quadric surfaces,
- ruled surfaces
Citation: Hamza Alzaareer, Hassan Al-Zoubi, Farhan Abdel-Fattah. Certain classifications on quadrics in simply isotropic space $ \mathbb{I}^{3} $[J]. AIMS Mathematics, 2025, 10(11): 26662-26679. doi: 10.3934/math.20251172

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Abstract

In this paper, we deal with the natural geometry of quadric surfaces in the isotropic space $ \mathbb{I}^{3} $. We provided defining equations for the $ 3^{rd}, 4^{th} $ type ruled surfaces and $ 1^{st}, 2^{nd} $ type of quadric surfaces. In this paper, we investigated the finite Chen-type of ruled and quadric surfaces in the 3-dimensional simply isotropic space $ \mathbb{I}^{3} $, corresponding to the third fundamental form of the surface.

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