On a type of semisymmetric metric connection on a Riemannian manifold

doi:10.2298/PIM150317025D

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On a type of semisymmetric metric connection on a Riemannian manifold

Journal Article•DOI•

On a type of semisymmetric metric connection on a Riemannian manifold

Uday De Chand¹, Ajit Barman•Institutions (1)

University of Calcutta¹

01 Jan 2015-Publications De L'institut Mathematique (National Library of Serbia)-Vol. 98, Iss: 112, pp 211-218

TL;DR: In this article, a semisymmetric metric connection on a Riemannian manifold whose torsion tensor is almost pseudo symmetric was studied, and the associated 1-form of the connection on the almost pseudo-symmetric manifold was derived.

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Abstract: We study a type of semisymmetric metric connection on a Riemannian manifold whose torsion tensor is almost pseudo symmetric and the associated 1-form of almost pseudo symmetric manifold is equal to the associated 1-form of the semisymmetric metric connection.

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Some semisymmetry conditions on Riemannian manifolds

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Ahmet Yildiz, Azime Çetinkaya

01 May 2014

TL;DR: In this article, a Riemannian manifold M admits a semisymmetric metric connection, such that the vector field U is a parallel unit vector field with respect to the Levi-Civita connection ∇.

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Abstract: We study a Riemannian manifold M admitting a semisymmetric metric connection ∇ such that the vector field U is a parallel unit vector field with respect to the Levi-Civita connection ∇. Firstly, we show that if M is projectively flat with respect to the semisymmetric metric connection ∇ then M is a quasi-Einstein manifold. Also we prove that if R⋅P=0 if and only if M is projectively semisymmetric; if P⋅R=0 or R⋅P-P⋅R=0 then M is conformally flat and quasi-Einstein manifold. Here R, P and P denote Riemannian curvature tensor, the projective curvature tensor of ∇ and the projective curvature tensor of ∇, respectively.

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3 citations

Cites background from "On a type of semisymmetric metric c..."

...For some properties of Riemannian manifolds with a semisymmetric metric connection (see also [1], [6], [4], [5], [7], [14], [21], [22])....
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Singular minimal translation surfaces in Euclidean spaces endowed with semi-symmetric connections

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Ayla Erdur, Muhittin Evren Aydin, Mahmut Ergüt

30 Oct 2020-arXiv: Differential Geometry

TL;DR: In this article, singular minimal translation surfaces in a Euclidean space of dimension 3 have been studied and classified with a certain semi-symmetric (non-)metric connection.

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Abstract: In this paper, we study and classify singular minimal translation surfaces in a Euclidean space of dimension 3 endowed with a certain semi-symmetric (non-)metric connection.

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2 citations

Additional excerpts

...For example, see [2], [3], [7], [9], [15], [18], [24], [42]-[45], [56], [57], [60]....
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Singular minimal surfaces which are minimal

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Muhittin Evren Aydin, Ayla Erdur, Mahmut Ergüt

19 Nov 2020-arXiv: Differential Geometry

TL;DR: In this paper, the singular minimal surfaces in a Euclidean 3-space R^{3} which are minimal are the generalized cylinders, providing their explicit equations, and a trivial outcome is observed when they use a special semi-symmetric non-metric connection instead of the Levi-Civita connection.

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Abstract: In the present paper, we discuss the singular minimal surfaces in a Euclidean 3-space R^{3} which are minimal. In fact, such a surface is nothing but a plane, a trivial outcome. However, a non-trivial outcome is obtained when we modify the usual condition of singular minimality by using a special semi-symmetric metric connection instead of the Levi-Civita connection on R^{3}. With this new connection, we prove that, besides planes, the singular minimal surfaces which are minimal are the generalized cylinders, providing their explicit equations. A trivial outcome is observed when we use a special semi-symmetric non-metric connection. Furthermore, our discussion is adapted to the Lorentz-Minkowski 3-space.

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1 citations

Cites background from "On a type of semisymmetric metric c..."

...Without giving a complete list, we may refer to [2], [3], [6], [9], [13],[14],...
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DOI•

Curvatures of semi-symmetric metric connections on statistical manifolds

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Mohammad Bagher Kazemi Balgeshir, Shiva Salahvarzi

01 Jan 2021

1 citations

Journal Article•DOI•

On golden semisymmetric metric FF-connections

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Aydin Gezer, Cagri Karaman

01 Jan 2017-Turkish Journal of Mathematics

TL;DR: In this paper, a semisymmetric metric F -connection on a locally decomposable golden Riemannian manifold was constructed and the curvature properties of the connection were investigated.

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Abstract: In this paper, we construct a golden semisymmetric metric F -connection on a locally decomposable golden Riemannian manifold and investigate some properties of its curvature, conharmonic curvature, Weyl projective curvature, and torsion tensors. Moreover, we define the transposed connection of this connection and study its curvature properties.

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1 citations

Cites background from "On a type of semisymmetric metric c..."

...Chaki and Konar [1] obtained the expression for the curvature tensor of a Riemannian manifold that admits a semisymmetric metric connection with vanishing curvature and recurrent torsion tensors....
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...References [1] Chaki MC, Konar A....
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References

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Hypersurfaces of a conformally flat space

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浩柳本

01 Mar 1972

86 citations

"On a type of semisymmetric metric c..." refers background or methods in this paper

...A Riemannian manifold of quasiconstant curvature was given by Chen and Yano [6] as a conformally flat manifold with the curvature tensor R̃ of type (0, 4) which satisfies the condition...
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...A Riemannian manifold of quasiconstant curvature was given by Chen and Yano [6] as a conformally flat manifold with the curvature tensor R̃ of type (0, 4) which satisfies the condition R̃(X, Y, Z, W ) = p[g(Y, Z)g(X, W ) − g(X, Z)g(Y, W )](1.6) + q[g(X, W )T (Y )T (Z) − g(X, Z)T (Y )T (W ) + g(Y, Z)T (X)T (W ) − g(Y, W )T (X)T (Z)], where p and q are scalar functions, T is a nonzero 1-form and λ is a unit vector field defined by g(X, λ) = T (X)....
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...Later Mocanu [15] pointed out that the manifold introduced by Chen and Yano [6] and the manifold introduced by Vranceanu [27] are the same....
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Journal Article•

On a type of semi-symmetric connection on a Riemannian manifold

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Uday Chand De

01 Jan 1990-Indian Journal of Pure & Applied Mathematics

74 citations

"On a type of semisymmetric metric c..." refers background in this paper

...M. C. Chaki, A. Konar, On a type of semi-symmetric connection on a Riemannian manifold, J. Pure Math., Calcutta University, (1981), 77–80....
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...The study of the semisymmetric metric connection was further developed by Yano [28], Amur and Pujar [1], Prvanović [19, 20, 21], Prvanović and Pušić [22], Chaki and Konar [5], De [8, 7], De and Biswas [11], De and De [9, 10], Sharfuddin and Hussain [25], Binh [2], Özen, Aynur and Altay [16], Ozgur and Sular [17, 18] and many others....
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Journal Article•DOI•

On semi-symmetric connections

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T. Q. Binh

01 Jun 1990-Periodica Mathematica Hungarica

33 citations

"On a type of semisymmetric metric c..." refers background in this paper

...L. Tamassy, T. Q. Binh, On weakly symmetric and weakly projective symmetric Riemannian manifolds, Colloq....
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...In this context, we can mention that the notion of weakly symmetric manifold was introduced by Tamassy and Binh [26]....
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...T. Q. Binh, On semi-symmetric connection, Period....
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...The study of the semisymmetric metric connection was further developed by Yano [28], Amur and Pujar [1], Prvanović [19, 20, 21], Prvanović and Pušić [22], Chaki and Konar [5], De [8, 7], De and Biswas [11], De and De [9, 10], Sharfuddin and Hussain [25], Binh [2], Özen, Aynur and Altay [16], Ozgur and Sular [17, 18] and many others....
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