Certain results of \((LCS)_n\)-manifolds endowed with \(E\)-Bochner curvature tensor. (English) Zbl 07905372
Summary: In this paper, we study geometry of \((LCS)_n\)-manifold focusing on some conditions of \(E\)-Bochner curvature tensor. First, we describe an \(E\)-Bochner pseudo-symmetric \((LCS)_n\)-manifold is never reduces to \(E\)-Bochner semi-symmetric manifold under the condition \((( \alpha^2- \rho)\neq 0)\). Next, we characterize certain results of \((LCS)_n\)-manifold satisfying \(B^{e}(U,V) \xi = 0\), \(B^{e}(\xi, V) \cdot B^e = 0\) and \(B^{e}(\xi, V) \cdot S = 0\).
MSC:
| 53C15 | General geometric structures on manifolds (almost complex, almost product structures, etc.) |
| 53C25 | Special Riemannian manifolds (Einstein, Sasakian, etc.) |
| 53C50 | Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics |
Keywords:
\(E\)-Bochner curvature tensor; \((LCS)_n\)-manifold; scalar curvature; \( \xi \)-sectional curvature; \( \eta \)-Einstein manifoldReferences:
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