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Legendre Matrix Method for Legendre Curve in Sasakian 3-Manifold

Aydin Tuba Ağirman, Sezer Mehmet, Kocayiğit Hüseyin

Foundations of Computing and Decision Sciences

2021

Vol. 46, No. 3

205--219

In this study, unit-speed the Legendre curves are studied in Sasakian 3-manifold. Firstly, differential equations characterizing the Legendre curves are obtained and the method used for the approximate solution is explained. Then, the approximate solution is found for one of the characterizations of the Legendre curve with the Legendre matrix collocation method. In addition, a sample application is made to make the method more understandable. And finally, with the help of these equations and the approximate solution, the geometric properties of this curve type are examined.

A dimensional restriction for a class of contact manifolds

Loiudice E.

Demonstratio Mathematica

2017

Vol. 50, nr 1

231--238

In this work we consider a class of contact manifolds (M, η) with an associated almost contact metric structure (φ, ξ, η, g). This class contains, for example, nearly cosymplectic manifolds and the manifolds in the class C9 ⊕ C10 defined by Chinea and Gonzalez. All manifolds in the class considered turn out to have dimension 4n + 1. Under the assumption that the sectional curvature of the horizontal 2-planes is constant at one point, we obtain that these manifolds must have dimension 5.