Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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DIAGONAL LIFTS OF TENSOR FIELDS OF TYPE (1,1) ON CROSS-SECTIONS IN TENSOR BUNDLES AND ITS APPLICATIONS

  • Gezer, Aydin (DEPARTMENT OF MATHEMATICS FACULTY OF ARTS AND SCIENCES ATATURK UNIVERSITY) ;
  • Salimov, Arif (DEPARTMENT OF MATHEMATICS FACULTY OF ARTS AND SCIENCES ATATURK UNIVERSITY)
  • Published : 2008.03.31
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Abstract

The main purpose of this paper is to investigate diagonal lift of tensor fields of type (1,1) from manifold to its tensor bundle of type (p, q) and to prove that when a manifold $M_n$ admits a $K\ddot{a}hlerian$ structure ($\varphi$,g), its tensor bundle of type (p,q) admits an complex structure.

Keywords

References

  1. N. Cengiz and A. A. Salimov, Complete lifts of derivations to tensor bundles, Bol. Soc. Mat. Mexicana (3) 8 (2002), no. 1, 75-82
  2. A. Ledger and K. Yano, Almost complex structures on tensor bundles, J. Differential Geometry 1 (1967), 355-368 https://doi.org/10.4310/jdg/1214428099
  3. A. Magden, N. Cengiz, and A. A. Salimov, Horizontal lift of affinor structures and its applications, Appl. Math. Comput. 156 (2004), no. 2, 455-461 https://doi.org/10.1016/j.amc.2003.08.004
  4. A. Magden and A. A. Salimov, Horizontal lifts of tensor fields to sections of the tangent bundle, Izv. Vyssh. Uchebn. Zaved. Mat. (2001), no. 3, 77-80
  5. A. Magden and A. A. Salimov, Horizontal lifts of tensor fields to sections of the tangent bundle, translation in Russian Math. (Iz. VUZ) 45 (2001), no. 3, 73-76
  6. A. A. Salimov, A new method in the theory of liftings of tensor fields in a tensor bundle, Izv. Vyssh. Uchebn. Zaved. Mat. (1994), no. 3, 69-75
  7. A. A. Salimov, A new method in the theory of liftings of tensor fields in a tensor bundle, translation in Russian Math. (Iz. VUZ) 38 (1994), no. 3, 67-73
  8. K. Yano and S. Ishihara, Tangent and Cotangent Bundles: Differential Geometry, Pure and Applied Mathematics, No. 16. Marcel Dekker, Inc., New York, 1973
  9. K. Yano and M. Kon, Structures on Manifolds, Series in Pure Mathematics, 3. World Scientific Publishing Co., Singapore, 1984

Cited by

  1. On operators associated with tensor fields vol.99, pp.1-2, 2010, https://doi.org/10.1007/s00022-010-0059-6
  2. On the (1, 1)-tensor bundle with Cheeger–Gromoll type metric vol.125, pp.4, 2015, https://doi.org/10.1007/s12044-015-0221-z