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1999 | 80 | 2 | 201-209
Tytuł artykułu

Pseudo-Bochner curvature tensor on Hermitian manifolds

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Our main purpose of this paper is to introduce a natural generalization $B_H$ of the Bochner curvature tensor on a Hermitian manifold $M$ provided with the Hermitian connection. We will call $B_H$ the pseudo-Bochner curvature tensor. Firstly, we introduce a unique tensor P, called the (Hermitian) pseudo-curvature tensor, which has the same symmetries as the Riemannian curvature tensor on a Kähler manifold. By using P, we derive a necessary and sufficient condition for a Hermitian manifold to be of pointwise constant Hermitian holomorphic sectional curvature. Our pseudo-Bochner curvature tensor $B_H$ is naturally obtained from the conformal relation for the pseudo-curvature tensor P and it is conformally invariant. Moreover we show that $B_H$ is different from the Bochner conformal tensor in the sense of Tricerri and Vanhecke.
Rocznik
Tom
80
Numer
2
Strony
201-209
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-10-13
Twórcy
autor
  • Department of Mathematics, Ichinoseki National College of Technology, Ichinoseki 021-8511, Japan
Bibliografia
  • [1] A. Balas, Compact Hermitian manifolds of constant holomorphic sectional curvature, Math. Z. 189 (1985), 193-210.
  • [2] S. Bochner, Curvature and Betti numbers, II, Ann. of Math. 50 (1949), 77-93.
  • [3] L. A. Cordero, M. Fernández and A. Gray, Symplectic manifolds with no Kähler structure, Topology 25 (1986), 375-380.
  • [4] G. Ganchev, S. Ivanov and V. Mihova, Curvatures on anti-Kaehler manifolds, Riv. Mat. Univ. Parma (5) 2 (1993), 249-256.
  • [5] S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vol. II, Interscience Publ., New York, 1969.
  • [6] K. Matsuo, Locally conformally Hermitian-flat manifolds, Ann. Global Anal. Geom. 13 (1995), 43-54.
  • [7] K. Matsuo, On local conformal Hermitian-flatness of Hermitian manifolds, Tokyo J. Math. 19 (1996), 499-515.
  • [8] S. Tachibana, On the Bochner curvature tensor, Nat. Sci. Rep. Ochanomizu Univ. 18 (1967), 15-19.
  • [9] F. Tricerri and L. Vanhecke, Curvature tensors on almost Hermitian manifolds, Trans. Amer. Math. Soc. 267 (1981), 365-398.
  • [10] I. Vaisman, Generalized Hopf manifolds, Geom. Dedicata 13 (1982), 231-255.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv80i2p201bwm
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