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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.

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.)

Citations:

Zbl 0799.53040
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