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On the geometry of conharmonic curvature tensor for nearly Kähler manifolds

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Abstract

We study additional symmetry properties for the harmonic curvature tensor of a nearly Kähler manifold. An exhaustive description for conharmonically para-Kählerian, nearly Kählerian manifolds, and conharmonically flat, nearly Kählerian manifolds is obtained.

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References

  1. M. Barros and A. Ramirez, “Decomposition of quasi-Kähler manifolds that satisfy the first curvature condition,” Demonstr. Math., 11, No. 3, 685–694 (1978).

    MathSciNet  MATH  Google Scholar 

  2. A. Gray, “Nearly Kähler manifolds,” J. Differ. Geom., 4, No. 3, 283–309 (1970).

    MATH  Google Scholar 

  3. A. Gray, “Curvature identities for Hermitian and almost Hermitian manifolds,” Tôhoku Math. J., 28, No. 4, 601–612 (1976).

    Article  MATH  Google Scholar 

  4. A. Gray, “The structures of nearly Kähler manifolds,” Ann. Math., 223, 233–248 (1976).

    Article  MATH  Google Scholar 

  5. A. Gray and L. Vanhecke, “Almost Hermitian manifolds with constant holomorphic sectional curvature,” Časopis Pěst. Mat., 104, No. 2, 170–179 (1979).

    MathSciNet  MATH  Google Scholar 

  6. Y. Ishii, “On conharmonic transformations,” Tensor, 7, No. 2, 73–80 (1957).

    MathSciNet  MATH  Google Scholar 

  7. V. F. Kirichenko, “Generalized quasi-Kählerian manifolds and axioms of CR-submanifolds and axioms of CR-submanifolds in generalized Hermitian geometry, II,” Geom. Dedicata, 52, 53–85 (1994).

    Article  MathSciNet  MATH  Google Scholar 

  8. V. F. Kirichenko, Differential-Geometrical Structures on Manifolds [in Russian], MSPU, Moscow (2003).

    Google Scholar 

  9. A. Naveira and L. M. Hervella, “Quasi-Kahler manifolds,” Proc. Am. Math. Soc., 49, No. 2, 327–333 (1975).

    MathSciNet  Google Scholar 

  10. G.-B. Rizza, “Varietà parakähleriane,” Ann. Mat. Pura Appl., 98, No. 4, 47–61 (1974).

    MathSciNet  MATH  Google Scholar 

  11. S. Sawaki and K. Sekigawa, “Almost Hermitian manifolds with constant holomorphic sectional curvature,” J. Differ. Geom., 9, 123–134 (1974).

    MathSciNet  MATH  Google Scholar 

  12. L. Vanhecke, “Almost Hermitian manifolds with J-invariant Riemann curvature tensor,” Rend. Sem. Mat. Univ. Politec. Torino, 34, 487–498 (1975–76).

    MathSciNet  Google Scholar 

  13. L. Vanhecke, “Some almost Hermitian manifolds with constant holomorphic sectional curvature,” J. Differ. Geom., 12, No. 4, 461–471 (1977).

    MathSciNet  MATH  Google Scholar 

  14. B. Watson and L. Vanhecke, “K1-curvatures and almost Hermitian submersions,” Rend. Sem. Mat. Univ. Politec. Torino, 36, 205–224 (1977–78).

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Moscow Pedagogical State University, Moscow, Russia

    V. F. Kirichenko & A. A. Shihab

Authors
  1. V. F. Kirichenko
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  2. A. A. Shihab
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Correspondence to V. F. Kirichenko or A. A. Shihab.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 16, No. 2, pp. 43–54, 2010.

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Kirichenko, V.F., Shihab, A.A. On the geometry of conharmonic curvature tensor for nearly Kähler manifolds. J Math Sci 177, 675–683 (2011). https://doi.org/10.1007/s10958-011-0495-3

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