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Affine connections on almost para-cosymplectic manifolds

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Abstract

Identities for the curvature tensor of the Levi-Cività connection on an almost para-cosymplectic manifold are proved. Elements of harmonic theory for almost product structures are given and a Bochner-type formula for the leaves of the canonical foliation is established.

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References

  1. C. L. Bejan, M. Ferrara: Para-Kähler manifolds of quasi-constant P-sectional curvature. Proceedings of the Conference Contemporary Geometry and Related Topics, Belgrade, Serbia and Montenegro, June 26–July 2, 2005 (N. Bokan, ed.). Cigoja Publishing Company, 2006, pp. 29–36.

  2. P. Dacko, Z. Olszak: On weakly para-cosymplectic manifolds of dimension 3. J. Geom. Phys. 57 (2007), 561–570.

    Article  MathSciNet  MATH  Google Scholar 

  3. S. Erdem: On almost (para)contact (hyperbolic) metric manifolds and harmonicity of (φ,φ′)-holomorphic maps between them. Houston J. Math. 28 (2002), 21–45.

    MathSciNet  MATH  Google Scholar 

  4. S. Funabashi, H. S. Kim, Y.-M. Kim, J. S. Pak: Traceless component of the conformal curvature tensor in Kähler manifold. Czech. Math. J. 56 (2006), 857–874.

    Article  MathSciNet  MATH  Google Scholar 

  5. W. Jianming: Harmonic complex structures. Chin. Ann. Math., Ser. A 30 (2009), 761–764; arXiv: 1007.4392v1/math.DG (2010).

    MATH  Google Scholar 

  6. Z. Olszak: On almost cosymplectic manifolds. Kodai Math. J. 4 (1981), 239–250.

    Article  MathSciNet  MATH  Google Scholar 

  7. M. Prvanović: Holomorphically projective transformations in a locally product space. Math. Balk. 1 (1971), 195–213.

    MATH  Google Scholar 

  8. L. Schäfer: tt*-bundles in para-complex geometry, special para-Kähler manifolds and para-pluriharmonic maps. Differ. Geom. Appl. 24 (2006), 60–89.

    Article  MATH  Google Scholar 

  9. Y. L. Xin: Geometry of Harmonic Maps. Progress in Nonlinear Differential Equations and Their Applications 23. Birkhäuser, Boston, 1996.

    Google Scholar 

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Correspondence to Adara M. Blaga.

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Blaga, A.M. Affine connections on almost para-cosymplectic manifolds. Czech Math J 61, 863–871 (2011). https://doi.org/10.1007/s10587-011-0033-y

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  • DOI: https://doi.org/10.1007/s10587-011-0033-y

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