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Displaying similar documents to “Some Properties of Lorentzian α -Sasakian Manifolds with Respect to Quarter-symmetric Metric Connection”

Some Classes of Lorentzian α -Sasakian Manifolds Admitting a Quarter-symmetric Metric Connection

Santu DEY, Buddhadev Pal, Arindam BHATTACHARYYA (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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The object of the present paper is to study a quarter-symmetric metric connection in an Lorentzian α -Sasakian manifold. We study some curvature properties of an Lorentzian α -Sasakian manifold with respect to the quarter-symmetric metric connection. We study locally φ -symmetric, φ -symmetric, locally projective φ -symmetric, ξ -projectively flat Lorentzian α -Sasakian manifold with respect to the quarter-symmetric metric connection.

Projective Curvature Tensorin 3-dimensional Connected Trans-Sasakian Manifolds

Krishnendu De, Uday Chand De (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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The object of the present paper is to study ξ -projectively flat and φ -projectively flat 3-dimensional connected trans-Sasakian manifolds. Also we study the geometric properties of connected trans-Sasakian manifolds when it is projectively semi-symmetric. Finally, we give some examples of a 3-dimensional trans-Sasakian manifold which verifies our result.

On generalized Douglas-Weyl Randers metrics

Tayebeh Tabatabaeifar, Behzad Najafi, Mehdi Rafie-Rad (2021)

Czechoslovak Mathematical Journal

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We characterize generalized Douglas-Weyl Randers metrics in terms of their Zermelo navigation data. Then, we study the Randers metrics induced by some important classes of almost contact metrics. Furthermore, we construct a family of generalized Douglas-Weyl Randers metrics which are not R -quadratic. We show that the Randers metric induced by a Kenmotsu manifold is a Douglas metric which is not of isotropic S -curvature. We show that the Randers metric induced by a Kenmotsu or Sasakian...

On a Semi-symmetric Metric Connection in an Almost Kenmotsu Manifold with Nullity Distributions

Gopal Ghosh, Uday Chand De (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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We consider a semisymmetric metric connection in an almost Kenmotsu manifold with its characteristic vector field ξ belonging to the ( k , μ ) ' -nullity distribution and ( k , μ ) -nullity distribution respectively. We first obtain the expressions of the curvature tensor and Ricci tensor with respect to the semisymmetric metric connection in an almost Kenmotsu manifold with ξ belonging to ( k , μ ) ' - and ( k , μ ) -nullity distribution respectively. Then we characterize an almost Kenmotsu manifold with ξ belonging to ( k , μ ) ' -nullity...

Curvature tensors and Ricci solitons with respect to Zamkovoy connection in anti-invariant submanifolds of trans-Sasakian manifold

Payel Karmakar (2022)

Mathematica Bohemica

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The present paper deals with the study of some properties of anti-invariant submanifolds of trans-Sasakian manifold with respect to a new non-metric affine connection called Zamkovoy connection. The nature of Ricci flat, concircularly flat, ξ -projectively flat, M -projectively flat, ξ - M -projectively flat, pseudo projectively flat and ξ -pseudo projectively flat anti-invariant submanifolds of trans-Sasakian manifold admitting Zamkovoy connection are discussed. Moreover, Ricci solitons on...

Classification of 4 -dimensional homogeneous weakly Einstein manifolds

Teresa Arias-Marco, Oldřich Kowalski (2015)

Czechoslovak Mathematical Journal

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Y. Euh, J. Park and K. Sekigawa were the first authors who defined the concept of a weakly Einstein Riemannian manifold as a modification of that of an Einstein Riemannian manifold. The defining formula is expressed in terms of the Riemannian scalar invariants of degree two. This concept was inspired by that of a super-Einstein manifold introduced earlier by A. Gray and T. J. Willmore in the context of mean-value theorems in Riemannian geometry. The dimension 4 is the most interesting...

On real flag manifolds with cup-length equal to its dimension

Marko Radovanović (2020)

Czechoslovak Mathematical Journal

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We prove that for any positive integers n 1 , n 2 , ... , n k there exists a real flag manifold F ( 1 , ... , 1 , n 1 , n 2 , ... , n k ) with cup-length equal to its dimension. Additionally, we give a necessary condition that an arbitrary real flag manifold needs to satisfy in order to have cup-length equal to its dimension.