대한수학회지 (Journal of the Korean Mathematical Society)

  • 제44권1호
  • /
  • Pages.237-247
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  • 2007
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  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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CONNECTIONS ON ALMOST COMPLEX FINSLER MANIFOLDS AND KOBAYASHI HYPERBOLICITY

  • Won, Dae-Yeon (Department of Mathematics Duksung Women's University) ;
  • Lee, Nany (Department of Mathematics The University of Seoul)
  • 발행 : 2007.01.31
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초록

In this paper, we establish a necessary condition in terms of curvature for the Kobayashi hyperbolicity of a class of almost complex Finsler manifolds. For an almost complex Finsler manifold with the condition (R), so-called Rizza manifold, we show that there exists a unique connection compatible with the metric and the almost complex structure which has the horizontal torsion in a special form. With this connection, we define a holomorphic sectional curvature. Then we show that this holomorphic sectional curvature of an almost complex submanifold is not greater than that of the ambient manifold. This fact, in turn, implies that a Rizza manifold is hyperbolic if its holomorphic sectional curvature is bounded above by -1.

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참고문헌

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피인용 문헌

  1. An almost paracontact structure on a Rizza manifold vol.349, pp.11-12, 2011, https://doi.org/10.1016/j.crma.2011.06.005