Abstract
AbstractThe three-dimensional pseudohermitian manifolds with positive, zero, and negative constant pseudohermitian sectional curvature, respectively, with vanishing pseudohermitian torsion are the Heisenberg group $$H_1$$
H
1
, the CR sphere $$S^3$$
S
3
, and the circle bundle $$B^1\times \mathbb {R}$$
B
1
×
R
. While the differential geometry of curves in $$H_1$$
H
1
and $$S^3$$
S
3
has been studied before, there has not been any study on the differential geometry of curves in $$B^1\times \mathbb {R}$$
B
1
×
R
. In this paper, we take the first step in this direction. Among other things, we find the explicit formulas of the p-curvature and T-variation for curves in $$B^1\times \mathbb {R}$$
B
1
×
R
. We also prove the fundamental theorem of curves in $$B^1\times \mathbb {R}$$
B
1
×
R
.
Funder
National Science and Technology Council
Publisher
Springer Science and Business Media LLC
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