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Dergiler / European Journal of Pure and Applied Mathematics (elektronik) / 2010 / Cilt: 3 - Sayı: 4

Almost Hermitian manifold with flat Bochner tensor

Habeeb M. ABOOD
Sayfa
0–0
Yayın Tarihi
2022-11-05
DOI
—
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Finally we prove that if M is flat manifold with flat Bochner tensor, then M is an Einstein manifold with a cosmological constant. 2000 Mathematics Subject Classifications: 53C55, 53B35

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:Many researchers investigated the flat Bochner tensor on some kinds of almost Hermitian manifold.
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Temel Bulgular & Veri:It is proved that if M is an almost Hermitian manifold of class R1 with flat Bochner tensor, then either M is 2-dimensional flat Ricci manifold or n-dimensional (n > 2) flat scalar curvature tensor manifold.
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Sonuç & Katkı:Finally we prove that if M is flat manifold with flat Bochner tensor, then M is an Einstein manifold with a cosmological constant. 2000 Mathematics Subject Classifications: 53C55, 53B35
🔬Tür:Araştırma Makalesi
📍Kapsam:2000 Verileri
⚙️Değişkenler:Alan Parametreleri

Abstract

Many researchers investigated the flat Bochner tensor on some kinds of almost Hermitian manifold. In the present paper the author studies this tensor on general class almost Hermitian manifold by using a new methodology which is called an adjoint G-structure space. Thus this study generalize the results which are found out by those researchers. It is proved that if M is an almost Hermitian manifold of class R1 with flat Bochner tensor, then either M is 2-dimensional flat Ricci manifold or n-dimensional (n > 2) flat scalar curvature tensor manifold. As well, it is proved that if M is an almost Hermitian manifold with flat Bochner tensor, then M is a manifold of class R3 if and only if M is a linear complex manifold. Later on, equivalently of classes R2 and R3 is investigated. Finally we prove that if M is flat manifold with flat Bochner tensor, then M is an Einstein manifold with a cosmological constant. 2000 Mathematics Subject Classifications: 53C55, 53B35

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Bu Makaleye Atıf Yap

ABOOD, H. M. (2022). Almost Hermitian manifold with flat Bochner tensor. European Journal of Pure and Applied Mathematics (elektronik), Cilt: 3 - Sayı: 4, 0–0. https://ajindex.com/articles/650426

Kaynakça (17)

  1. A. Al-Otman and V. F. Kirichenko, On the geometry of the Bochner tensor of Nearly Kahler, Russian Mathematical Surveys V.48, p.155-156. 1993
  2. V. I. Arnold, Mathematical methods of classical mechanics, Springer. 1989
  3. S. Bochner, Curvature and Betti numbers, II, Ann of Math., V.50, p.77-93. 1949
  4. A. Gray,Curvature identities for Hermitian and almost Hermitian manifolds, Tohoku Math.J. V. p.601-612. 1976
  5. V. F. Kirichenko, New results of K-spaces theory, Ph.D.thesis, Moscow State University. 1975
  6. V. F. Kirichenko, K-spaces of constant type,Seper. Math. J. V.17 No.2, p.282-289. 1976
  7. S. Kobayashi and K. Nomizu, Foundation of differential geometry, V2, John Wiley and sons. 1969
  8. M. Mastumoto, On Kahlerian spaces with parallel or vanishing curvature tensor,Tensor, N. S. V.20, p. 25-28. 1969
  9. K. Nam, Note on Kahlerian manifold whose Bochner curvature tensor vanishes, Bull. Korean Math. Soc., 25, No.1, p.99-105. 1988
  10. Z. Olsag, Bochner flat manifolds, Diff. geom. Banash C. P., V.12, p.219-223. 1984
  11. M. Petrovic and L. Vestraclen, On the concircular tensor, the projective curvature tensor of Bochner-Kahler manifolds, Math. Rep. Toyama Univ., V.10, p.37-61. 1987
  12. G. B Rizza, Varieta Parakahleriane, Ann. Math. Pura et Appl., V.98, No.4, p.47-61. 1974
  13. M. C. Sean, The cosmological conatant, Irr, Max-Planek Institut Fur Gravitations Physik, 1. 2001
  14. S. Tachibana, On Bochner curvature tensor, Not. Sci. Ochanomidzu Univ., V.18, p.15-19. 1967
  15. S. Tachibana, Notes on Kahlerian metrics with Vanishing Bochner curvature tensor, Kodi Math. Semin. Repts., V.22, p.313-321. 1970
  16. E. V. Tretiakova, Curvature identities for Almost Kahler manifold, VINITE, Moscow, No.208-B99. 1999 [17] L. Vanhecke, Some almost Hermitian manifolds with constant holomorphic sectional curvature, J. Diff. Geom., V.12, No.4, p.461-467. 1977
  17. L. Vanhecke, The Bochner curvature tensor on almost Hermitian manifold, Hokkaido Math. J., V.7, No.2, p.252-258. 1987.