On deformed Riemannian extensions associated with twin Norden metrics

Abstract

The main purpose of this paper is to study the deformed Riemannian extension g+V G •• in the cotangent bundle, where G is a twin Norden metric on the base manifold.

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References

  1. [1]

    Aras, M., The metric connection with respect to the synectic metric, Hacet. J. Math. Stat., 41(2), 2012, 169–173.

    MATH  MathSciNet  Google Scholar 

  2. [2]

    Aslanci, S., Kazimova, S. and Salimov, A. A., Some notes concerning Riemannian extensions, Ukrainian Math. J., 62(5), 2010, 661–675.

    Article  MathSciNet  Google Scholar 

  3. [3]

    Bonome, A., Castro, R., Hervella, L. M. and Matsushita, Y., Construction of Norden structures on neutral 4-manifolds, JP J. Geom. Topol., 5(2), 2005, 121–140.

    MATH  MathSciNet  Google Scholar 

  4. [4]

    Salimov, A., Tensor Operators and Their Applications, Nova Science Publishers, New York, 2012.

    Google Scholar 

  5. [5]

    Talantova, N. V. and Shirokov, A. P., A remark on a certain metric in the tangent bundle, Izv. Vys. Ucebn. Zaved. Matematika, 157(6), 1975, 143–146.

    Google Scholar 

  6. [6]

    Vishnevskii, V. V., Shirokov, A. P. and Shurygin, V. V., Spaces over Algebras, Kazanskii Gosudarstvennyi Universitet, Kazan, 1985.

    Google Scholar 

  7. [7]

    Yano, K. and Ishihara, S., Tangent and Cotangent Bundles, Mercel Dekker, Inc., New York, 1973.

    Google Scholar 

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Correspondence to Arif Salimov.

Additional information

This work was supported by the Scientific and Technological Research Council of Turkey (MFAG-1001, No. 112T111).

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Salimov, A., Cakan, R. On deformed Riemannian extensions associated with twin Norden metrics. Chin. Ann. Math. Ser. B 36, 345–354 (2015). https://doi.org/10.1007/s11401-015-0914-8

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Keywords

  • Riemannian extension
  • Cotangent bundle
  • Vertical and complete lifts
  • Horizontal lifts
  • Deformed metric
  • Twin Norden metric

2000 MR Subject Classification

  • 55R10
  • 53C07