Legendre Curves on Generalized Paracontact Metric Manifolds
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Two different notions of almost paracontact structures (which are compatible or anti-compatible with the metric), well known in the literature, are unified and generalized here. Several formulas of paraholomorphic maps are established, and a result of Lichnerowicz type is obtained. The connection transformations which have the same system of paracontact-planar Legendre curves are characterized. Conformal changes of metrics which preserve geodesics (resp. paracontact-planar Legendre curves) are studied.
KeywordsParacontact structures on manifolds Linear connection Geodesics Planar curve Harmonic map
Mathematics Subject Classification53C15 53B05 53C22 53C43
Cornelia-Livia Bejan was supported by the Scientific and Technical Research Council of Turkey (TUBITAK). As a visiting Professor in İnönü University, Malatya, Cornelia-Livia Bejan thanks members of Math. Department for their kind hospitality. The authors thank the referee for careful reading of the manuscript.
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