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Some Curvature Conditions on a Para-Sasakian Manifold with Canonical Paracontact Connection

Author

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  • Bilal Eftal Acet
  • Erol Kılıç
  • Selcen Yüksel Perktaş

Abstract

We study canonical paracontact connection on a para-Sasakian manifold. We prove that a Ricci-flat para-Sasakian manifold with respect to canonical paracontact connection is an -Einstein manifold. We also investigate some properties of curvature tensor, conformal curvature tensor, -curvature tensor, concircular curvature tensor, projective curvature tensor, and pseudo-projective curvature tensor with respect to canonical paracontact connection on a para-Sasakian manifold. It is shown that a concircularly flat para-Sasakian manifold with respect to canonical paracontact connection is of constant scalar curvature. We give some characterizations for pseudo-projectively flat para-Sasakian manifolds.

Suggested Citation

  • Bilal Eftal Acet & Erol Kılıç & Selcen Yüksel Perktaş, 2012. "Some Curvature Conditions on a Para-Sasakian Manifold with Canonical Paracontact Connection," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-24, December.
    • Handle: RePEc:hin:jijmms:395462
    DOI: 10.1155/2012/395462
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