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Legendre Curves on Generalized Paracontact Metric Manifolds

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Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. Department of Mathematics, “Gh. Asachi” Technical University, Bd. Carol I, No. 11, Corp A, 700506, Iasi, Romania

    Cornelia-Livia Bejan

  2. Seminarul Matematic, Universitatea “Alexandru Ioan Cuza”, Bd. Carol I, No. 11, 700506, Iasi, Romania

    Cornelia-Livia Bejan

  3. Department of Mathematics, Mersin University, 33343, Mersin, Turkey

    Şemsi Eken Meriç

  4. Department of Mathematics, İnönü University, 44280, Malatya, Turkey

    Erol Kılıç

Authors
  1. Cornelia-Livia Bejan
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  2. Şemsi Eken Meriç
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  3. Erol Kılıç
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Correspondence to Cornelia-Livia Bejan.

Additional information

Communicated by Young Jin Suh.

Dedicated to Professor Old $$\check{\text {r}}$$ r ˇ ich Kowalski on the occasion of his 80th birthday.

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Bejan, CL., Eken Meriç, Ş. & Kılıç, E. Legendre Curves on Generalized Paracontact Metric Manifolds. Bull. Malays. Math. Sci. Soc. 42, 185–199 (2019). https://doi.org/10.1007/s40840-017-0475-y

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  • DOI: https://doi.org/10.1007/s40840-017-0475-y

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