Constancy of holomorphic sectional curvature in Pseudo-Kähler manifolds
| Autor: | R. K. Nagaich, S. I. Husain |
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| Rok vydání: | 1984 |
| Předmět: | |
| Zdroj: | Volume: 33, Issue Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics |
| ISSN: | 1303-5991 2618-6470 |
| DOI: | 10.1501/commua1_0000000574 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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