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Journal ArticleDOI

On Almost Generalized Weakly Symmetric LP-Sasakian Manifolds

TL;DR: In this article, the existence of an almost generalized weakly symmetric LP-Sasakian manifold is proved by a non-trivial example, and the notions of weakly Ricci-symmetric LP S-Sakian manifolds are introduced.
Abstract: Abstract The purpose of this paper is to introduce the notions of an almost generalized weakly symmetric LP-Sasakian manifolds and an almost generalized weakly Ricci-symmetric LP-Sasakian manifolds. The existence of an almost generalized weakly symmetric LP-Sasakian manifold is ensured by a non-trivial example.

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Citations
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Journal ArticleDOI
01 Dec 2019
TL;DR: In this paper, the authors investigated the Ricci solitons on D -homothetically deformed Kenmotsu manifold with generalized weakly symmetric and generalized Ricci symmetric curvature restrictions.
Abstract: The object of the present paper is to investigate the nature of Ricci solitons on D -homothetically deformed Kenmotsu manifold with generalized weakly symmetric and generalized weakly Ricci symmetric curvature restrictions.

11 citations

Journal ArticleDOI
23 Dec 2020
TL;DR: In this paper, the notions of almost generalized weakly symmetric and almost generalized Ricci-symmetric π-cosymplectic manifolds have been studied and analyzed.
Abstract: In the present paper, we study the notions of an almost generalized weakly symmetric $\alpha$-cosymplectic manifolds and an almost generalized weakly Ricci-symmetrik $\alpha$-cosymplectic manifolds.

1 citations

Journal ArticleDOI
TL;DR: In this paper, the authors introduced the notion of generalized weakly φ-symmetric and generalized weak weakly Ricci φ symmetric Lorentzian Para Sasakian manifold.
Abstract: The present paper attempt to introduce the notion of generalized weakly φ-symmetric and generalized weakly Ricci φ-symmetric Lorentzian Para Sasakian manifold. Furthermore, we have studied generalized weakly φ-symmetric Lorentzian Para-Sasakian spacetimes. In addition, the existence of generalized weakly φ-symmetric Lorentzian Para Sasakian manifold is ensured by a suitable example. AMS Mathematics Subject Classification (2010): 53C15; 53C25

1 citations


Additional excerpts

  • ...(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
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Journal ArticleDOI

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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01 Jan 1988

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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Journal Article
TL;DR: In this article, a study of Lorentzian almost paracontact manifolds with a structure of the concircular type is presented, where the structure is of the form
Abstract: This paper presents a study of Lorentzian almost paracontact manifolds with a structure of the concircular type.

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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01 Apr 2007

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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