Research Article
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Year 1984, Volume: 33 , - , 01.01.1984
https://doi.org/10.1501/Commua1_0000000574

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  • Communications, Series A1:Mathematics and Statistics

Constancy of holomorphic sectional curvature in Pseudo-Kähler manifolds

Year 1984, Volume: 33 , - , 01.01.1984
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.

References

  • Communications, Series A1:Mathematics and Statistics
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Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

R. K Nagaıch This is me

Publication Date January 1, 1984
Submission Date January 1, 1984
Published in Issue Year 1984 Volume: 33

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APA Nagaıch, R. K. (1984). Constancy of holomorphic sectional curvature in Pseudo-Kähler manifolds. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 33. https://doi.org/10.1501/Commua1_0000000574
AMA Nagaıch RK. Constancy of holomorphic sectional curvature in Pseudo-Kähler manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. January 1984;33. doi:10.1501/Commua1_0000000574
Chicago Nagaıch, R. K. “Constancy of Holomorphic Sectional Curvature in Pseudo-Kähler Manifolds”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 33, January (January 1984). https://doi.org/10.1501/Commua1_0000000574.
EndNote Nagaıch RK (January 1, 1984) Constancy of holomorphic sectional curvature in Pseudo-Kähler manifolds. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 33
IEEE R. K. Nagaıch, “Constancy of holomorphic sectional curvature in Pseudo-Kähler manifolds”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 33, 1984, doi: 10.1501/Commua1_0000000574.
ISNAD Nagaıch, R. K. “Constancy of Holomorphic Sectional Curvature in Pseudo-Kähler Manifolds”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 33 (January 1984). https://doi.org/10.1501/Commua1_0000000574.
JAMA Nagaıch RK. Constancy of holomorphic sectional curvature in Pseudo-Kähler manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 1984;33. doi:10.1501/Commua1_0000000574.
MLA Nagaıch, R. K. “Constancy of Holomorphic Sectional Curvature in Pseudo-Kähler Manifolds”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 33, 1984, doi:10.1501/Commua1_0000000574.
Vancouver Nagaıch RK. Constancy of holomorphic sectional curvature in Pseudo-Kähler manifolds. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 1984;33.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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