R. K NAGAICH

Constancy of holomorphic sectional curvature in Pseudo-Kähler manifolds

ISSN: 1303-5991
Yayın Aralığı: Yılda 4 Sayı
Başlangıç: 1948
Yayıncı: Ankara Üniversitesi

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.

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