COSYMPLECTIC MANIFOLDS WITH AN INDEFINITE RIEMANNIAN METRIC

  • Lee, Sang-Deok (Department of Mathematics College of Natural Science Dankook University) ;
  • Jun, Dong-Kum (Department of Mathematics College of Natural Science Soonchunhyang University) ;
  • Kim, Byung-Hak (Department of Mathematics and Institute of Natural Sciences Kyung Hee University)
  • Published : 1999.03.01

Abstract

Graves and Nomizu investigated an indefinite version of the Cartan's result. Specifically they obtained the conditions for all non-degenerate planes to have the same sectional curvature in the in-definite Riemannian manifold. In this paper we are to study the cosym-plective version of the results of Graves and Nomizu and characterize an indefinite cosymplectic spce form.

Keywords

References

  1. Lecons Sur la geometric des espaces de Riemann E.Cartan
  2. J. Math. Pures Appl. v.72 Topology of cosymplectic manifolds D. Chinea;M. Deleon;J.C. Marrero
  3. J.Math Pures Appl. v.72 Topology of cosymplectic manifolds D.Chinea;M.Deleon;J.C.Marrero
  4. Bull. Korean Math. Soc. v.9 Cosymplectic manifolds of constant φ-holomorphic curvature S.S.Eum
  5. Introduction to modern differential geometry (in Japanese) K.Nomizu
  6. H. Math. Ann v.247 On sectional curvature of indefinite mtrics II M.Dajczer;K.Nomizu
  7. Math. Ann. v.232 On sectional curvature of indefinite metrices L.Graves;K.Nomizu
  8. Comm.de la Faculte des. Sc.1 Univ. d'Ankara Serie A v.Tome 33 Annee Constancy of holomorphic sectional curvature in pseudo-Kaehler manifolds R.K.Nagaichi;S.I.Husain
  9. Semi-Riemannian geometry with application to relativity B.O'Neill