In this paper we studied quadric surfaces in the Euclidean 3-space that were of finite type with respect to the second fundamental form Ⅱ. The main result presented in this article was that spheres were the only quadric surfaces of finite type. This indicated a specific and notable classification within the broader category of quadric surfaces based on their finite type characteristics in relation to the second fundamental form.
Citation: Mutaz Al-Sabbagh. Quadric surfaces of finite Chen Ⅱ-type[J]. AIMS Mathematics, 2024, 9(12): 34435-34446. doi: 10.3934/math.20241640
In this paper we studied quadric surfaces in the Euclidean 3-space that were of finite type with respect to the second fundamental form Ⅱ. The main result presented in this article was that spheres were the only quadric surfaces of finite type. This indicated a specific and notable classification within the broader category of quadric surfaces based on their finite type characteristics in relation to the second fundamental form.
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Mutaz Al-Sabbagh. Quadric surfaces of finite Chen Ⅱ-type[J]. AIMS Mathematics, 2024, 9(12): 34435-34446. doi: 10.3934/math.20241640
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