Analysis of Gaudi surfaces at small deformations

Velimirović, Ljubica S.; Cvetković, Milica; Ćirić, Marija S.; Velimirović, Nikola

doi:10.1016/j.amc.2011.12.005

Cited by 12 publications

(5 citation statements)

References 2 publications

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“…The problems of infinitesimal bending of curves and surfaces in Euclidean 3‐space

{normal𝔼}^{3}

are an important part of differential geometry and are discussed in [8–19, 21–24] and so forth. Based on these considerations, primarily on papers [11, 17, 22, 24], we will generalize the basic concepts and statements to dual 3‐space

{normal𝔻}^{3}

.…”

Section: Infinitesimal Bending Of Dual Curvesmentioning

confidence: 99%

“…There are many papers related to deformations of ruled surfaces. For instance, in [18], the authors deal with a special class of ruled surfaces under infinitesimal bending and give explicit formulas for the bending field. With E. Study's mapping in mind, an interesting question arises: Can small deformations of ruled surfaces be observed through corresponding small deformations of dual spherical curves?…”

Section: Introductionmentioning

confidence: 99%

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Characterization of dual curves using the theory of infinitesimal bending

Najdanović

2024

Math Methods in App Sciences

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In this paper, we generalize the main ideas and statements of the theory of infinitesimal bending in Euclidean 3‐space to dual curves in the dual 3‐space . The basic condition we introduce is the invariance of the dual arc length with appropriate precision. Necessary and sufficient conditions for the dual field to be an infinitesimal bending field are given. Some useful formulas and facts about dual arc length and dual bending field are obtained. An explicit characterization of the dual spherical curve bending is presented, and the corresponding infinitesimal bending field is decomposed into dual vectors of the dual Frenet frame. Finally, some examples are given to illustrate our results.

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“…The problems of infinitesimal bending of curves and surfaces in Euclidean 3‐space

{normal𝔼}^{3}

{normal𝔻}^{3}

.…”

Section: Infinitesimal Bending Of Dual Curvesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Characterization of dual curves using the theory of infinitesimal bending

Najdanović

2024

Math Methods in App Sciences

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“…A concept of infinitesimal bending of surfaces and curves is very interesting in mathematics and is applied in mechanics, physics, biology, medicine, architecture, etc. For instance, papers [16] and [17] present the applications of infinitesimal bending in biology, article [18] presents its application in architecture. During the infinitesimal bending of curves are obtained the ruled surfaces [5].…”

Section: Introductionmentioning

confidence: 99%

Infinitesimal bending of DNA helices

Maksimović¹,

Velimirović²,

Najdanović³

2021

Turk J Math

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The mathematics of DNA molecules is often studied as a double helix model. This paper focuses on the modelling of infinitesimal bending of DNA helices. The paper checks the flexibility of DNA molecule, i.e. the flexibility of double helix in infinitesimal bending theory. Actually, first, we find infinitesimal bending field of an arbitrary curve on the helicoid, that leaves bent curves on the helicoid, and show that helix bending on the helicoid is not possible.Finally, we deal with the infinitesimal bending of helicoid, using PDEs. Visualization of infinitesimal bending was done in Mathematica.

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“…Therefore we will deal more with the study of V 2 , i. e. the inner geometry of S 2 . For recent studies of the deformation of surfaces from a different point, see [3,7,[20][21][22][23][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

On the existence of isoperimetric extremals of rotation and the fundamental equations of rotary diffeomorphisms

Mikeš

Sochor

Stepanova

2015

Filomat

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In this paper we study the existence and the uniqueness of isoperimetric extremals of rotation on two-dimensional (pseudo-) Riemannian manifolds and on surfaces on Euclidean space. We find the new form of their equations which is easier than results by S. G. Leiko. He introduced the notion of rotary diffeomorphisms. In this paper we propose a new proof of the fundamental equations of rotary mappings.

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Analysis of Gaudi surfaces at small deformations

Cited by 12 publications

References 2 publications

Characterization of dual curves using the theory of infinitesimal bending

Characterization of dual curves using the theory of infinitesimal bending

Infinitesimal bending of DNA helices

On the existence of isoperimetric extremals of rotation and the fundamental equations of rotary diffeomorphisms

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