• 제목/요약/키워드: generalized weakly symmetric manifold

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ON GENERALIZED WEAKLY SEMI-CONFORMALLY SYMMETRIC MANIFOLDS

  • Hui, Shyamal Kumar;Patra, Akshoy;Patra, Ananta
    • 대한수학회논문집
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    • 제36권4호
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    • pp.771-782
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    • 2021
  • In this paper we introduce generalized weakly semi-conformally symmetric manifold, a generalization of weakly symmetric manifold. We study some basic properties and obtain the forms of the scalar curvature of such manifold. In the last section an example is given to ensure the existence of such manifold.

ON WEAKLY CYCLIC GENERALIZED B-SYMMETRIC MANIFOLDS

  • Mohabbat Ali;Aziz Ullah Khan;Quddus Khan;Mohd Vasiulla
    • 대한수학회논문집
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    • 제38권4호
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    • pp.1271-1280
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    • 2023
  • The object of the present paper is to introduce a type of non-flat Riemannian manifold, called a weakly cyclic generalized B-symmetric manifold (W CGBS)n. We obtain a sufficient condition for a weakly cyclic generalized B-symmetric manifold to be a generalized quasi Einstein manifold. Next we consider conformally flat weakly cyclic generalized B-symmetric manifolds. Then we study Einstein (W CGBS)n (n > 2). Finally, it is shown that the semi-symmetry and Weyl semi-symmetry are equivalent in such a manifold.

INVARIANT SUBMANIFOLDS OF (LCS)n-MANIFOLDS ADMITTING CERTAIN CONDITIONS

  • Eyasmin, Sabina;Baishya, Kanak Kanti
    • 호남수학학술지
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    • 제42권4호
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    • pp.829-841
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    • 2020
  • The object of the present paper is to study the invariant submanifolds of (LCS)n-manifolds. We study generalized quasi-conformally semi-parallel and 2-semiparallel invariant submanifolds of (LCS)n-manifolds and showed their existence by a non-trivial example. Among other it is shown that an invariant submanifold of a (LCS)n-manifold is totally geodesic if the second fundamental form is any one of (i) symmetric, (ii) recurrent, (iii) pseudo symmetric, (iv) almost pseudo symmetric and (v) weakly pseudo symmetric.