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 Loxodromes and transformations in pseudo-Hermitian geometry Commun. Korean Math. Soc. 2021 Vol. 36, No. 4, 817-827 https://doi.org/10.4134/CKMS.c200349Published online March 9, 2021Printed October 31, 2021 Ji-Eun Lee Chonnam National University Abstract : In this paper, we prove that a diffeomorphism $f$ on a normal almost contact $3$-manifold $M$ is a CRL-{\it transformation} if and only if $M$ is an $\alpha$-Sasakian manifold. Moreover, we show that a $CR$-loxodrome in an $\alpha$-Sasakian $3$-manifold is a pseudo-Hermitian magnetic curve with a strength $q=\widetilde{r}\eta(\gamma')=(r+\alpha-t)\eta(\gamma')$ for constant $\eta(\gamma')$. A non-geodesic $CR$-loxodrome is a non-Legendre slant helix. Next, we prove that let $M$ be an $\alpha$-Sasakian $3$-manifold such that $(\nabla_Y S)X=0$ for vector fields $Y$ to be orthogonal to $\xi$, then the Ricci tensor $\rho$ satisfies $\rho=2\alpha^2 g$. Moreover, using the CRL-{\it transformation} $\widetilde{\nabla}^t$ we fine the pseudo-Hermitian curvature $\widetilde{R}$, the pseudo-Ricci tensor $\widetilde{\rho}$ and the torsion tensor field $\widetilde{ \mathfrak{T}}^{t} (\widetilde{S}X,Y)$. Keywords : Loxodrome, magnetic curves, normal almost contact manifold, pseudo-Hermitian geometry MSC numbers : Primary 58E20, 53B25 Supported by : The author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2019R1l1A1A01043457). Downloads: Full-text PDF   Full-text HTML

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