• 제목/요약/키워드: Ricci-recurrent

검색결과 24건 처리시간 0.019초

Conformally Flat Totally Umbilical Submanifolds in Some Semi-Riemannian Manifolds

  • Ewert-Krzemieniewski, Stanislaw
    • Kyungpook Mathematical Journal
    • /
    • 제48권2호
    • /
    • pp.183-194
    • /
    • 2008
  • We prove that totally umbilical submanifold M of an extended quasi-recurren manifold is also extended quasi-recurrent. If, moreover, M is conformally flat then, locally, M is isometric to the manifold with known metric. Some curvature properties of such submanifold are investigated. Making use of these results we shall prove the existence of totally umbilical submanifold being pseudosymmetric in the sense of Ryszard Deszcz and satisfying some other curvature conditions.

NEARLY SASAKIAN MANIFOLD SATISFYING

  • Kim, Chong-Hon;Kim, Byong-Du
    • 대한수학회보
    • /
    • 제21권1호
    • /
    • pp.21-26
    • /
    • 1984
  • The notion of nearly Sasakian manifold was introduced in [1] and Z-Olszak has studied certain properties in [2] and [3]. In section (2) of this paper, we show that a nearly Sasakian manifold M admitting .GAMMA.$_{ji}$ $^{h}$ such that .del.$_{1}$ $R_{kji}$$^{h}$ =0 is of contant scalar curvature and the covariant derivate of the Ricci tensor of M is a symmetric tensor. In the last section, we shall deal with a recurrent and conformal recurrent nearly Sasakian manifold.d.

  • PDF

SPACETIMES ADMITTING DIVERGENCE FREE m-PROJECTIVE CURVATURE TENSOR

  • Uday Chand De;Dipankar Hazra
    • 대한수학회논문집
    • /
    • 제39권1호
    • /
    • pp.201-210
    • /
    • 2024
  • This paper is concerned with the study of spacetimes satisfying div 𝓜 = 0, where "div" denotes the divergence and 𝓜 is the m-projective curvature tensor. We establish that a perfect fluid spacetime with div 𝓜 = 0 is a generalized Robertson-Walker spacetime and vorticity free; whereas a four-dimensional perfect fluid spacetime becomes a Robertson-Walker spacetime. Moreover, we establish that a Ricci recurrent spacetime with div 𝓜 = 0 represents a generalized Robertson-Walker spacetime.