Infinitesimal F-planar transformations

Hinterleitner, Irena; Mikeš, Josef; Stránská, Jana

doi:10.3103/s1066369x08040026

Cited by 27 publications

(10 citation statements)

References 2 publications

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“…Infinitesimal bending of surfaces and manifolds was widely studied in (Aleksandrov, 1936;Alexandrov, 2010;Efimov, 1948;Hinterleitner et al, 2008;Ivanova-Karatopraklieva & Sabitov, 1995;Kon-Fossen, 1959;Najdanović, 2014;Vekua, 1959;Velimirović, 2009). Infinitesimal bending of curves was considered in (Efimov, 1948;Najdanovic, 2015;Najdanovic & Velimirovic, 2017a,b;Rancic et al, 2009;Velimirović, 2001aVelimirović, ,b, 2009Velimirović et al, 2010;Yano et al, 1946).…”

Section: Introductionmentioning

confidence: 99%

Infinitesimal bending of curves on the ruled surfaces

Najdanović¹,

Velimirović²

2018

Univ thought Publ nat sci

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In this paper we study infinitesimal bending of curves that lie on the ruled surfaces in Euclidean 3-dimensional space. We obtain an infinitesimal bending field under whose effect all bent curves remain on the same ruled surface as the initial curve. Specially, we consider infinitesimal bending of the curves which belong to the cylinder as well as to the hyperbolic paraboloid and find corresponding infinitesimal bending fields. We examine the variation of the curvature of a curve under infinitesimal bending on the hyperbolic paraboloid. Some examples are visualized using program packet Mathematica.

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Section: Introductionmentioning

confidence: 99%

Infinitesimal bending of curves on the ruled surfaces

Najdanović¹,

Velimirović²

2018

Univ thought Publ nat sci

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“…where x h are the coordinates of a certain point in V n andx h are the coordinates of its image under the infinitesimal transformation, ε is an infinitesimal parameter not depending on x h , and ξ h is a displacement vector, see [2,12]. If a certain object A of the space V n depends on x ∈ V n but also on the infinitesimal parameter ε, then the principal part of the object A is A 0 (x) + A 1 (x)ε in the expansion of series with respect to the infinitesimal…”

Section: Basic Definition Of Infinitesimal Rotary Transformationmentioning

confidence: 99%

“…The paper concerns with a study of infinitesimal rotary transformations [8], for other exmaples of infinitesimal transformations see also [2,12,[15][16][17][18][19][20]. The rotary diffeomorphism and rotary transformations of two-dimensional Riemannian spaces were first introduced by Leiko [4,5,7,11].…”

Section: Introductionmentioning

confidence: 99%

Infinitesimal rotary transformation

Rýparová

Mikeš

2019

Filomat

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The paper is devoted to further study of a certain type of infinitesimal transformations of twodimensional (pseudo-) Riemannian spaces, which are called rotary. An infinitesimal transformation is called rotary if it maps any geodesic on (pseudo-) Riemannian space onto an isoperimetric extremal of rotation in their principal parts on (pseudo-) Riemannian space. We study basic equations of the infinitesimal rotary transformations in detail and obtain the simpler fundamental equations of these transformations.

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“…This method was used for infinitesimal F -planar transformations [7]. In this paper we will consider the first and the second variation of a magnitude under infinitesimal bending of the second order.…”

Section: Definition 2 ([14]mentioning

confidence: 99%