DOI QR코드

DOI QR Code

KÄHLER SUBMANIFOLDS WITH LOWER BOUNDED TOTALLY REAL BISECTIONL CURVATURE TENSOR II

  • Pyo, Yong-Soo (Division of Mathematical Sciences Pukyong National University) ;
  • Shin, Kyoung-Hwa (Division of Mathematical Sciences Pukyong National University)
  • 발행 : 2002.04.01

초록

In this paper, we prove that if every totally real bisectional curvature of an n($\geq$3)-dimensional complete Kahler submanifold of a complex projective space of constant holomorphic sectional curvature c is greater than (equation omitted) (3n$^2$+2n-2), then it is totally geodesic and compact.

키워드

참고문헌

  1. J.Ramanujan Math.Soc. v.1 Complex submanifolds of an indefinite complex space form R.Aiyama;J.H.Kwon;H.Nakagawa
  2. Trans.Amer.Math.Soc. v.112 some implications of the generalized Gauss-Bonnet theorem R.L.Bishop;S.I.Goldberg https://doi.org/10.2307/1994158
  3. J.Differential Geometry v.1 Holomorphic bisectional curvature S.I.Goldberg;S.Kobayashi https://doi.org/10.4310/jdg/1214428090
  4. Pro.Amer.Math.Soc. v.56 On Totally real bisectional curvature B.S.Houh https://doi.org/10.2307/2041615
  5. J.Kor.Math.Soc. v.33 On semi-Kaehler manifolds whose totally real bisectional curvature is bounded from below U.H.Ki;Y.J.Suh
  6. Foundation of Differential Geometry Ⅰand Ⅱ S.Kobayashi;K.Nomizu
  7. Advances in Math. v.13 Differential geometry of Kaehler submanifolds K.Ogiue https://doi.org/10.1016/0001-8708(74)90066-8
  8. J.Math.Soc.Japan v.19 Isometric immersions of Riemannian manifolds H.Omori https://doi.org/10.2969/jmsj/01920205
  9. Lecture Notes in Math Kaehler submanifolds in the complex projective space, Differential Geometry, Peniscola 1985, 259-274 A.Ros
  10. Proc.Japan Acad. v.33 On Kaehlerian manifolds with positive holomorphic sectional curvature Y.Tsukamoto https://doi.org/10.3792/pja/1195525029
  11. Comm.Pure and Appl.Math. v.28 Harmonic functions on complete Riemannian manifolds S.T.Yau https://doi.org/10.1002/cpa.3160280203