Displaying similar documents to “Clifford approach to metric manifolds”

Generalized Einstein manifolds

Formella, Stanisław

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[For the entire collection see Zbl 0699.00032.] A manifold (M,g) is said to be generalized Einstein manifold if the following condition is satisfied ( ∇ X S ) ( Y , Z ) = σ ( X ) g ( Y , Z ) + ν ( Y ) g ( X , Z ) + ν ( Z ) g ( X , Y ) where S(X,Y) is the Ricci tensor of (M,g) and σ (X), ν (X) are certain ℓ -forms. In the present paper the author studies properties of conformal and geodesic mappings of generalized Einstein manifolds. He gives the local classification of generalized Einstein manifolds when g( ψ (X), ψ (X)) ≠ 0 .

Some Properties of Lorentzian α -Sasakian Manifolds with Respect to Quarter-symmetric Metric Connection

Santu DEY, Arindam BHATTACHARYYA (2015)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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The aim of this paper is to study generalized recurrent, generalized Ricci-recurrent, weakly symmetric and weakly Ricci-symmetric, semi-generalized recurrent, semi-generalized Ricci-recurrent Lorentzian α -Sasakian manifold with respect to quarter-symmetric metric connection. Finally, we give an example of 3-dimensional Lorentzian α -Sasakian manifold with respect to quarter-symmetric metric connection.

A contact metric manifold satisfying a certain curvature condition

Jong Taek Cho (1995)

Archivum Mathematicum

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In the present paper we investigate a contact metric manifold satisfying (C) ( ∇ ¯ γ ˙ R ) ( · , γ ˙ ) γ ˙ = 0 for any ∇ ¯ -geodesic γ , where ∇ ¯ is the Tanaka connection. We classify the 3-dimensional contact metric manifolds satisfying (C) for any ∇ ¯ -geodesic γ . Also, we prove a structure theorem for a contact metric manifold with ξ belonging to the k -nullity distribution and satisfying (C) for any ∇ ¯ -geodesic γ .