Metric Connection

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Mobin Ahmad - One of the best experts on this subject based on the ideXlab platform.

Cihan Özgür - One of the best experts on this subject based on the ideXlab platform.

Abdul Haseeb - One of the best experts on this subject based on the ideXlab platform.

Jae-bok Jun - One of the best experts on this subject based on the ideXlab platform.

C. S. Bagewadi - One of the best experts on this subject based on the ideXlab platform.

  • on φ recurrent para sasakian manifold admitting quarter symMetric Metric Connection
    2014
    Co-Authors: K Pradeep T Kumar, C. S. Bagewadi
    Abstract:

    The idea of Metric Connection with torsion in a Riemannian manifold was introduced by Hayden 1 . Further, some properties of semisymMetric Metric Connection have been studied by Yano 2 . In 3 , Golab defined and studied quarter-symMetric Connection on a differentiable manifold with affine Connection, which generalizes the idea of semisymMetric Connection. Various properties of quarter-symMetric Metric Connection have been studied by many geometers like Rastogi 4, 5 , Mishra and Pandey 6 , Yano and Imai 7 , De et al. 8, 9 , Pradeep Kumar et al. 10 , and many others. The notion of local symmetry of a Riemannian manifold has been weakened by many authors in several ways to a different extent. As a weaker version of local symmetry, Takahashi 11 introduced the notion of local φ-symmetry on a Sasakian manifold. Generalizing the notion of φ-symmetry, the authors De et al. 12 introduced the notion of φrecurrent Sasakian manifolds. A linear Connection ∇ on an n-dimensional differentiable manifold is said to be a quarter-symMetric Connection 3 if its torsion tensor T is of the form

  • Some Classes of Kenmotsu Manifolds with Respect to Semi-symMetric Metric Connection
    Acta Mathematica Sinica English Series, 2013
    Co-Authors: Doddabhadrappla Gowda Prakasha, C. S. Bagewadi, Aysel Turgut Vanli, D. A. Patil
    Abstract:

    In this paper, we study conharmonic curvature tensor in Kenmotsu manifolds with respect to semi-symMetric Metric Connection and also characterize conharmonically flat, conharmonically semisymMetric and ϕ-conharmonically flat Kenmotsu manifolds with respect to semi-symMetric Metric Connection.

  • Invariant Submanifolds of Sasakian Manifolds Admitting Semi-symMetric Metric Connection
    Communications in Mathematics and Applications, 2013
    Co-Authors: B. S. S. Anitha, C. S. Bagewadi
    Abstract:

    The object of this paper is to study invariant submanifolds $M$ of Sasakian manifolds $\widetilde{M}$ admitting a semi-symMetric Metric Connection and to show that $M$ admits semi-symMetric Metric Connection. Further it is proved that the second fundamental forms $\sigma$ and $\overline{\sigma}$ with respect to Levi-Civita Connection and semi-symMetric Metric Connection coincide. It is shown that if the second fundamental form $\sigma$ is recurrent, 2-recurrent, generalized 2-recurrent and $M$ has parallel third fundamental form with respect to semi-symMetric Metric Connection, then $M$ is totally geodesic with respect to Levi-Civita Connection.

  • On -Recurrent Para-Sasakian Manifold AdmittingQuarter-SymMetric Metric Connection
    ISRN Geometry, 2012
    Co-Authors: K. T. Pradeep Kumar, Venkatesha, C. S. Bagewadi
    Abstract:

    We obtained the relation between the Riemannian Connection and the quarter-symMetric Metric Connection on a para-Sasakian manifold. Further, we study