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Ukrainian Mathematical Journal

, Volume 65, Issue 7, pp 1122–1125 | Cite as

On the Geometry of Holomorphic Developable Vector Fields on Almost Hermitian Manifolds

  • V. F. Kirichenko
  • V. M. Kuzakon’
Brief Communications

The determination of conditions for the invariance of geometric objects under the action of a group of transformations is one of the most important problems of geometric research. We study the invariance conditions for almost Hermitian structures relative to the action of a local one-parameter group of diffeomorphisms generated by a developable vector field on a manifold. Moreover, we investigate the relationship between developable (in particular, concircular) vector fields on Riemannian manifolds and locally concircular transformations of the metric of these manifolds.

Keywords

Riemannian Manifold Ahlerian Manifold Hermitian Structure Riemannian Structure HERMITIAN Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    A.V. Aminova, Projective Transformations of Pseudo-Riemannian Manifolds [in Russian], Yanus-K, Moscow (2003).Google Scholar
  2. 2.
    E. Kaehler, “Uber eine bemerkenswerte Hermitische Metrik,” Abh. Math. Sem. Hamburgischen Univ., 9, 173–186 (1933).CrossRefGoogle Scholar
  3. 3.
    K. Yano, “Concircular geometry. I–4,” Proc. Imp. Acad. Jpn., 16, 195–200, 354–360, 442–448, 505–511 (1940).Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • V. F. Kirichenko
    • 1
  • V. M. Kuzakon’
    • 2
  1. 1.Moscow State Pedagogic UniversityMoscowRussia
  2. 2.Odessa National Academy of Food TechnologiesOdessaUkraine

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