Constancy of holomorphic sectional curvature in Pseudo-Kähler manifolds

Authors : R K NAGAICH

Pages : 0-0

Doi:10.1501/Commua1_0000000574

View : 45 | Download : 10

Publication Date : 1984-01-01

Article Type : Research Paper

Abstract :Cartan [1 ] had proved that a Riemannian Manifold is of constant curvature if Rinsert ignore into journalissuearticles values(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 insert ignore into journalissuearticles values(M, J); is of constant Holomorphic Sectional Curvature if Rinsert ignore into journalissuearticles values(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 Rinsert ignore into journalissuearticles values(X,JX); X is proportional to JX.
Keywords : holomorphic, Pseudo Kähler, manifolds

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