Constant curvature surfaces in a pseudo-isotropic space
2018 ◽
Vol 49
(3)
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pp. 221-233
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Keyword(s):
In this study, we deal with the local structure of curves and surfaces immersed in a pseudo-isotropic space $\mathbb{I}_{p}^{3}$ that is a particular Cayley-Klein space. We provide the formulas of curvature, torsion and Frenet trihedron for spacelike and timelike curves, respectively. The causal character of all admissible surfaces in $\mathbb{I}_{p}^{3}$ has to be timelike up to its absolute. We introduce the formulas of Gaussian and mean curvature for timelike surfaces in $\mathbb{I}_{p}^{3}$. As applications, we describe the surfaces of revolution which are the orbits of a plane curve under a hyperbolic rotation with constant Gaussian and mean curvature.
2016 ◽
Vol 71
(6)
◽
pp. 242-247
1887 ◽
Vol 23
(140)
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pp. 35-45
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1984 ◽
Vol 36
(3)
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pp. 427-437
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1989 ◽
pp. 91-94
2009 ◽
Vol 247
(4)
◽
pp. 1043-1063
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1983 ◽
Vol 34
(1)
◽
pp. 1-6
Keyword(s):
1972 ◽
Vol 78
(2)
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pp. 247-251
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2015 ◽
Vol 8
(1)
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pp. 116-127