Tbilisi Mathematical Journal

On three dimensional quasi-Sasakian manifolds

Nandan Ghosh and Manjusha Tarafdar

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Abstract

Let M be a 3-dimensional quasi-Sasakian manifold. Olszak [6] proved that M is conformally flat with constant scalar curvature and hence its structure function $\beta$ is constant. We have shown that in such M, a second order symmetric parallel tensor is a constant multiple of the associated metric tensor. A necessary and sufficient condition for such a manifold to be minimal has been obtained. Finally if such M satisfies $R(X,Y).S =0$, then, S has two different non-zero eigen values.

Article information

Source
Tbilisi Math. J., Volume 9, Issue 1 (2016), 23-28.

Dates
Received: 17 July 2015
Accepted: 18 December 2015
First available in Project Euclid: 12 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1528769039

Digital Object Identifier
doi:10.1515/tmj-2016-0003

Mathematical Reviews number (MathSciNet)
MR3459008

Zentralblatt MATH identifier
1335.53059

Subjects
Primary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)
Secondary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)

Keywords
Quasi-Sasakian manifold Eigen values

Citation

Ghosh, Nandan; Tarafdar, Manjusha. On three dimensional quasi-Sasakian manifolds. Tbilisi Math. J. 9 (2016), no. 1, 23--28. doi:10.1515/tmj-2016-0003. https://projecteuclid.org/euclid.tbilisi/1528769039


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References

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