• Title/Summary/Keyword: Ricci-recurrent

Search Result 24, Processing Time 0.027 seconds

BIHARMONIC HYPERSURFACES WITH RECURRENT OPERATORS IN THE EUCLIDEAN SPACE

  • Esmaiel, Abedi;Najma, Mosadegh
    • Bulletin of the Korean Mathematical Society
    • /
    • v.59 no.6
    • /
    • pp.1595-1603
    • /
    • 2022
  • We show how some of well-known recurrent operators such as recurrent curvature operator, recurrent Ricci operator, recurrent Jacobi operator, recurrent shape and Weyl operators have the significant role for biharmonic hypersurfaces to be minimal in the Euclidean space.

ON GENERALIZED W3 RECURRENT RIEMANNIAN MANIFOLDS

  • Mohabbat Ali;Quddus Khan;Aziz Ullah Khan;Mohd Vasiulla
    • Honam Mathematical Journal
    • /
    • v.45 no.2
    • /
    • pp.325-339
    • /
    • 2023
  • The object of the present work is to study a generalized W3 recurrent manifold. We obtain a necessary and sufficient condition for the scalar curvature to be constant in such a manifold. Also, sufficient condition for generalized W3 recurrent manifold to be special quasi-Einstein manifold are given. Ricci symmetric and decomposable generalized W3 recurrent manifold are studied. Finally, the existence of such a manifold is ensured by a non-trivial example.

A study on the geometry of 2-dimensional re-manifold $X_2$

  • Hwang, In-Ho
    • Journal of the Korean Mathematical Society
    • /
    • v.32 no.2
    • /
    • pp.301-309
    • /
    • 1995
  • Manifolds with recurrent connections have been studied by many authors, such as Chung, Datta, E.M.Patterson, M.Prvanovitch, Singal, and TAkano, etc (refer to [2] and [3]). Examples of such manifolds are those of recurrent curvature, Ricci-recurrent manifolds, and birecurrent manifolds.

  • PDF

SOME RESULTS ON (LCS)n-MANIFOLDS

  • Shaikh, Absos Ali
    • Journal of the Korean Mathematical Society
    • /
    • v.46 no.3
    • /
    • pp.449-461
    • /
    • 2009
  • The object of the present paper is to study $(LCS)_n$-manifolds. Several interesting results on a $(LCS)_n$-manifold are obtained. Also the generalized Ricci recurrent $(LCS)_n$-manifolds are studied. The existence of such a manifold is ensured by several non-trivial new examples.

A TYPE OF WEAKLY SYMMETRIC STRUCTURE ON A RIEMANNIAN MANIFOLD

  • Kim, Jaeman
    • Korean Journal of Mathematics
    • /
    • v.30 no.1
    • /
    • pp.61-66
    • /
    • 2022
  • A new type of Riemannian manifold called semirecurrent manifold has been defined and some of its geometric properties are studied. Among others we show that the scalar curvature of semirecurrent manifold is constant and hence semirecurrent manifold is also concircularly recurrent. In addition, we show that the associated 1-form (resp. the associated vector field) of semirecurrent manifold is closed (resp. an eigenvector of its Ricci tensor). Furthermore, we prove that if a Riemannian product manifold is semirecurrent, then either one decomposition manifold is locally symmetric or the other decomposition manifold is a space of constant curvature.

CONFORMALLY RECURRENT SPACE-TIMES ADMITTING A PROPER CONFORMAL VECTOR FIELD

  • De, Uday Chand;Mantica, Carlo Alberto
    • Communications of the Korean Mathematical Society
    • /
    • v.29 no.2
    • /
    • pp.319-329
    • /
    • 2014
  • In this paper we study the properties of conformally recurrent pseudo Riemannian manifolds admitting a proper conformal vector field with respect to the scalar field ${\sigma}$, focusing particularly on the 4-dimensional Lorentzian case. Some general properties already proven by one of the present authors for pseudo conformally symmetric manifolds endowed with a conformal vector field are proven also in the case, and some new others are stated. Moreover interesting results are pointed out; for example, it is proven that the Ricci tensor under certain conditions is Weyl compatible: this notion was recently introduced and investigated by one of the present authors. Further we study conformally recurrent 4-dimensional Lorentzian manifolds (space-times) admitting a conformal vector field: it is proven that the covector ${\sigma}_j$ is null and unique up to scaling; moreover it is shown that the same vector is an eigenvector of the Ricci tensor. Finally, it is stated that such space-time is of Petrov type N with respect to ${\sigma}_j$.