The generalized Smarandache ruled surfaces generated by Legendre curves in the Euclidean 3-space

Rong Zhao; Donghe Pei; Rong Zhao; Donghe Pei

doi:10.3934/math.20261275

AIMS Mathematics

2026, Volume 11, Issue 10: 32430-32449. doi: 10.3934/math.20261275

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Research article

The generalized Smarandache ruled surfaces generated by Legendre curves in the Euclidean 3-space

Rong Zhao ,
Donghe Pei ^,

School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China

Received: 15 July 2026 Revised: 11 September 2026 Accepted: 28 September 2026 Published: 09 October 2026
MSC : 53A05, 57R45, 58K05

By Smarandache geometry, this paper introduces a class of ruled surfaces that are generated from spherical Legendre curves in the Euclidean 3-space. The developability and minimality of the generalized Smarandache ruled surface are investigated, as well as the geometric properties of the base curve. Moreover, since Legendre curves admit singularities, the generated ruled surfaces also contain singularities. Therefore, the singularities of the generalized Smarandache ruled surface are analyzed via the theory of framed curves and framed surfaces.
- generalized Smarandache ruled surfaces,
- Legendre curves,
- singularities
Citation: Rong Zhao, Donghe Pei. The generalized Smarandache ruled surfaces generated by Legendre curves in the Euclidean 3-space[J]. AIMS Mathematics, 2026, 11(10): 32430-32449. doi: 10.3934/math.20261275

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Abstract

By Smarandache geometry, this paper introduces a class of ruled surfaces that are generated from spherical Legendre curves in the Euclidean 3-space. The developability and minimality of the generalized Smarandache ruled surface are investigated, as well as the geometric properties of the base curve. Moreover, since Legendre curves admit singularities, the generated ruled surfaces also contain singularities. Therefore, the singularities of the generalized Smarandache ruled surface are analyzed via the theory of framed curves and framed surfaces.

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