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On the geometry of the (1, 1)-tensor bundle with Sasaki type metric

Chinese Annals of Mathematics, Series B volume 32, pages 369–386 (2011)Cite this article

Abstract

Curvature properties are studied for the Sasaki metric on the (1, 1) tensor bundle of a Riemannian manifold. As an application, examples of almost para-Nordenian and para-Kähler-Nordenian B-metrics are constructed on the (1, 1) tensor bundle by looking at the Sasaki metric. Also, with respect to the para-Nordenian B-structure, paraholomorphic conditions for the complete lifts of vector fields are analyzed.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Ataturk University, 25240, Erzurum, Turkey

    Arif Salimov & Aydin Gezer

Authors
  1. Arif Salimov
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  2. Aydin Gezer
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Correspondence to Aydin Gezer.

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Project supported by the Scientific and Technological Research Council of Turkey (No. TBAG-108T590).

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Salimov, A., Gezer, A. On the geometry of the (1, 1)-tensor bundle with Sasaki type metric. Chin. Ann. Math. Ser. B 32, 369–386 (2011). https://doi.org/10.1007/s11401-011-0646-3

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  • DOI: https://doi.org/10.1007/s11401-011-0646-3

Keywords

  • Tensor bundle
  • Sasaki metric
  • Vertical and horizontal lift
  • B-manifold

2000 MR Subject Classification

  • 55R10
  • 53C07
  • 53C15