SOME CLASSES OF 3-DIMENSIONAL NORMAL ALMOST PARACONTACT METRIC MANIFOLDS

• Journal title : Honam Mathematical Journal
• Volume 37, Issue 4,  2015, pp.457-468
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2015.37.4.457
Title & Authors
SOME CLASSES OF 3-DIMENSIONAL NORMAL ALMOST PARACONTACT METRIC MANIFOLDS
ERKEN, I. KUPELI;

Abstract
The aim of present paper is to investigate 3-dimensional $\small{{\xi}}$-projectively flt and $\small{\tilde{\varphi}}$-projectively flt normal almost paracontact metric manifolds. As a first step, we proved that if the 3-dimensional normal almost paracontact metric manifold is $\small{{\xi}}$-projectively flt then $\small{{\Delta}{\beta}=0}$. If additionally $\small{{\beta}}$ is constant then the manifold is $\small{{\beta}}$-para-Sasakian. Later, we proved that a 3-dimensional normal almost paracontact metric manifold is $\small{\tilde{\varphi}}$-projectively flt if and only if it is an Einstein manifold for $\small{{\alpha},{\beta}=const}$. Finally, we constructed an example to illustrate the results obtained in previous sections.
Keywords
normal almost paracontact metric manifold;curvarure tensor;$\small{{\xi}}$-projectively flat;$\small{{\varphi}}$-projectively flat;para-Sasakian manifold;Einstein manifold;
Language
English
Cited by
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