On Legendre curves in Riemannian and Lorentzian Sasaki spaces. (English) Zbl 1013.53016

Belkhelfa, M.; Hirică, I. E.; Rosca, R.; Verstraelen, L.

Soochow J. Math. 28, No. 1, 81-91 (2002).

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.)

Keywords:

Legendre curves; contact manifolds; Saskian structures

Citations:

Zbl 0799.53040