Constancy of holomorphic sectional curvature in Pseudo-Kähler manifolds

Year 1984, Volume: 33 , - , 01.01.1984

R. K Nagaıch

https://doi.org/10.1501/Commua1_0000000574

Abstract

Cartan [1 ] had proved that a Riemannian Manifold is of constant curvature if R(X,Y, X,Z) = 0 for every orthonormal triplet X,Y and Z. Graves and Nomizu [2 ] have extended this result to Pseudo-Riemannian Manifold. In the present paper this result has been extended to Kahler Manifolds with indefinite metric by proving that: “A Pseudo-Kahler manifold (M, J) is of constant Holomorphic Sectional Curvature if R(X,Y,X,JX) = 0 whenever X,Y and JX are ortbonormal” . A result of Tannö [4 ] on Almost Hermitian Manifold has also been extended to Pseudo-Kahler Manifolds by proving that a criterian for constancy of Holomorphic Sectio­ nal Curvature is that R(X,JX) X is proportional to JX.

Keywords

holomorphic, Pseudo-Kähler, manifolds

References

• Communications, Series A1:Mathematics and Statistics