On Legendre curves in Riemannian and Lorentzian Sasaki spaces. (English) Zbl 1013.53016
A 1-dimensional integral submanifold of a contact manifold is said to be a Legendre curve. Some results on Legendre curves, obtained for the Riemannian Sasaki spaces by C. Baikoussis and D. E. Blair [Geom. Dedicata 49, 135-142 (1994; Zbl 0799.53040)] are extended now to the Lorentzian case. In particular, the 3-dimensional-Sasaki-Heisenberg spaces are involved. In the latter all biharmonic Legendre curves are classified.
Reviewer: Ülo Lumiste (Tartu)
MSC:
| 53B30 | Local differential geometry of Lorentz metrics, indefinite metrics |
| 53C25 | Special Riemannian manifolds (Einstein, Sasakian, etc.) |
| 53C42 | Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) |
