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 Proper Helix of Order 6 And LC Helix in Pseudo-Euclidean Space E84

Buddhadev Pal (1) and Santosh Kumar (2)

(1,2) Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi-221005, India

Email address: (1) pal.buddha@gmail.com

Email address: (2) thakursantoshbhu@gmail.com

Doi : https://doi.org/10.47013/15.4.19

Cited by : Jordan J. Math & Stat., 15 (4B) (2022), 1077 - 1092

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Received on: Oct. 21, 2021;                                             Accepted on: April 14, 2022

 Abstract. In this paper, we used the result that complex hyperbolic spaces CH2 (−4c/3) with holomorphic sectional curvature −4c/3 are isometrically embedded in E84 . By considering a circle in CH2(−4c/3), we prove that the image of the circle by isometric embedding is a proper helix of order 6 in E84. Moreover, we define a generalized LC helix on a submanifold of E84. Also, we show that the image of a circle by isometric embedding from complex hyperbolic plane CH2(−4c/3) to pseudo-Euclidean space E84 is a generalized LC helix on some submanifold of E84.

Keywords: Curve of proper order, complex hyperbolic space, generalized LC helix, isometric embedding, parallel second fundamental form.