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2013•Mathematics and StatisticsOpen access

SOME CURVATURE CONDITIONS ON α-COSYMPLECTIC MANIFOLDS

Hakan Öztürk

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Abstract

The main interest of the present paper is to study α-cosymplectic manifolds that satisfy some certain tensor conditions. In particular, we consider α-cosymplectic manifolds with flatness conditions. We prove that there can not exist ϕ-projectively flat α-cosymplectic manifolds whose scalar curvature is zero for the dimension is greater than three. Furthermore, we work with special weakly Ricci-symmetric α-cosymplectic manifolds. We conclude the paper with an example on α-cosymplectic manifolds.

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What this paper is about

The main interest of the present paper is to study α-cosymplectic manifolds that satisfy some certain tensor conditions. In particular, we consider α-cosymplectic manifolds with flatness conditions. We prove that there can not exist ϕ-projectively flat α-cosymplectic manifolds whose scalar curvature is zero for the dimension is greater than three. Furthermore, we work with special weakly Ricci-symmetric α-cosymplectic manifolds. We conclude the paper with an example on α-cosymplectic manifolds.

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Available abstract

The main interest of the present paper is to study α-cosymplectic manifolds that satisfy some certain tensor conditions. In particular, we consider α-cosymplectic manifolds with flatness conditions. We prove that there can not exist ϕ-projectively flat α-cosymplectic manifolds whose scalar curvature is zero for the dimension is greater than three. Furthermore, we work with special weakly Ricci-symmetric α-cosymplectic manifolds. We conclude the paper with an example on α-cosymplectic manifolds.

Key concepts: Mathematics, Curvature, Mathematical analysis, Pure mathematics, Geometry

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