On Almost Generalized Weakly Symmetric LP-Sasakian Manifolds
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...(vi) generalized pseudo φ-symmetric space in the sense of [1] (for A2 = B = D = H1 6= 0, α2 = β = γ = H2 6= 0), (vii) semi-pseudo φ-symmetric space in the sense of [30] ( A = α = β = γ = 0, B = D 6= 0), (viii) generalized semi-pseudo φ-symmetric space in the sense of [3] ( A = 0 = α, B = D 6= 0, β = γ 6= 0), (ix) almost pseudo φ-symmetric space in the sense of [6] (for A = H1 + K1, B = D = H1 6= 0 and α = β = γ = 0), (x) almost generalized pseudo φ-symmetric space in the sense of [3]( A = H1 +K1, B = D = H1 6= 0, α = H2 +K2, β = γ = H2 6= 0), (xi) weakly φ-symmetric space in the sense of [29] ( for A, B, D 6= 0, α = β = γ = 0)....
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References
204 citations
"On Almost Generalized Weakly Symmet..." refers background in this paper
...The beauty of such A(GWS)n-manifold is that it has the flavour of (i) locally symmetric space in the sense of Cartan (for Ai = Bi = Ci = Di = 0), (ii) recurrent space by Walker [13](for A1 6= 0, A2 = Bi = Ci = Di = 0), (iii) generalized recurrent space by Dubey [14] (Ai 6= 0 and Bi = Ci = Di = 0), (iv) pseudo symmetric space by Chaki [11] (for A1 = B1 = C1 = D1 6= 0 and A2 = B2 = C2 = D2 = 0), (v) semi-pseudo symmetric space in the sense of Tarafder et al....
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...The beauty of such A(GWS)n-manifold is that it has the flavour of (i) locally symmetric space in the sense of Cartan (for Ai = Bi = Ci = Di = 0), (ii) recurrent space by Walker [13](for A1 6= 0, A2 = Bi = Ci = Di = 0), (iii) generalized recurrent space by Dubey [14] (Ai 6= 0 and Bi = Ci = Di = 0), (iv) pseudo symmetric space by Chaki [11] (for A1 = B1 = C1 = D1 6= 0 and A2 = B2 = C2 = D2 = 0), (v) semi-pseudo symmetric space in the sense of Tarafder et al. [10] (for A1 = −B1, C1 = D1 and A2 = B2 = C2 = D2 = 0), (vi) generalized semi-pseudo symmetric space in the sense of Baishya [6] (for A1 = −B1, C1 = D1 and A2 = −B2, C2 = D2), (vii) generalized pseudo symmetric space, by Baishya [5] (for Ai = Bi = Ci = Di 6= 0), (viii) almost pseudo symmetric space in the sprite of Chaki et al. [12] (for B1 6= 0, A1 = C1 = D1 6= 0 and A2 = B2 = C2 = D2 = 0), (ix) almost generalized pseudo symmetric space in the sense of Baishya (for Bi 6= 0, Ai = Ci = Di 6= 0) and (x) weakly symmetric space by Tamássy and Binh [16] ( for A1 = A2 = B2 = C2 = D2 = 0)....
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...[13] A. G. Walker, On Ruse’s space of recurrent curvature, Proc. of London Math....
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126 citations
"On Almost Generalized Weakly Symmet..." refers background in this paper
...The beauty of such A(GWS)n-manifold is that it has the flavour of (i) locally symmetric space in the sense of Cartan (for Ai = Bi = Ci = Di = 0), (ii) recurrent space by Walker [13](for A1 6= 0, A2 = Bi = Ci = Di = 0), (iii) generalized recurrent space by Dubey [14] (Ai 6= 0 and Bi = Ci = Di = 0), (iv) pseudo symmetric space by Chaki [11] (for A1 = B1 = C1 = D1 6= 0 and A2 = B2 = C2 = D2 = 0), (v) semi-pseudo symmetric space in the sense of Tarafder et al....
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...The beauty of such A(GWS)n-manifold is that it has the flavour of (i) locally symmetric space in the sense of Cartan (for Ai = Bi = Ci = Di = 0), (ii) recurrent space by Walker [13](for A1 6= 0, A2 = Bi = Ci = Di = 0), (iii) generalized recurrent space by Dubey [14] (Ai 6= 0 and Bi = Ci = Di = 0), (iv) pseudo symmetric space by Chaki [11] (for A1 = B1 = C1 = D1 6= 0 and A2 = B2 = C2 = D2 = 0), (v) semi-pseudo symmetric space in the sense of Tarafder et al. [10] (for A1 = −B1, C1 = D1 and A2 = B2 = C2 = D2 = 0), (vi) generalized semi-pseudo symmetric space in the sense of Baishya [6] (for A1 = −B1, C1 = D1 and A2 = −B2, C2 = D2), (vii) generalized pseudo symmetric space, by Baishya [5] (for Ai = Bi = Ci = Di 6= 0), (viii) almost pseudo symmetric space in the sprite of Chaki et al. [12] (for B1 6= 0, A1 = C1 = D1 6= 0 and A2 = B2 = C2 = D2 = 0), (ix) almost generalized pseudo symmetric space in the sense of Baishya (for Bi 6= 0, Ai = Ci = Di 6= 0) and (x) weakly symmetric space by Tamássy and Binh [16] ( for A1 = A2 = B2 = C2 = D2 = 0)....
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...[11] M. C. Chaki, On pseudo Ricci symmetric manifolds, Bulg....
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...[12] M. C. Chaki and T. Kawaguchi, On almost pseudo Ricci symmetric manifolds, Tensor, 58(1), (2007), 10–14....
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63 citations
"On Almost Generalized Weakly Symmet..." refers background in this paper
...This type of manifold is also discussed in ([2], [3]) An n-dimensional differentiable manifold M is said to be an LP-Sasakian manifold [1] if it admits a (1, 1) tensor field φ, a unit timelike contravarit vector field ξ, a 1-form η and a Lorentzian metric g which satisfy η(ξ) = −1, g(X, ξ) = η(X), φ(2)X = X + η(X)ξ, (2....
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...Then the following relations hold ([1], [15]) : g(R(X, Y )Z, ξ) = η(R(X, Y )Z) = g(Y, Z)η(X)− g(X,Z)η(Y ), (2....
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...Matsumoto ([1]) introduced the notion of Lorentzian para-Sasakian (LP-Sasakian for short) manifold....
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...Also, since the vector field η is closed in an LP-Sasakian manifold, we have ([1], [15])...
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39 citations
"On Almost Generalized Weakly Symmet..." refers background in this paper
...[12] (for B1 6= 0, A1 = C1 = D1 6= 0 and A2 = B2 = C2 = D2 = 0), (ix) almost generalized pseudo symmetric space in the sense of Baishya (for Bi 6= 0, Ai = Ci = Di 6= 0) and...
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...In analogy to [12], a weakly symmetric Riemannian manifold (M, g)(n > 2), is said to be an almost weakly pseudo symmetric manifold, if its curvature tensor R̄ of type (0, 4) is not identically zero and satisfies the identity...
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22 citations