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Legendre curves on 3-dimensional Kenmotsu manifolds admitting semisymmetric metric connection. (English) Zbl 1499.53173

Summary: The object of the present paper is to study biharmonic Legendre curves, locally \(\phi\)-symmetric Legendre curves and slant curves in 3-dimensional Kenmotsu manifolds admitting semisymmetric metric connection. Finally, we construct an example of a Legendre curve in a 3-dimensional Kenmotsu manifold.

MSC:

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
53D10 Contact manifolds (general theory)
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