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Scientific paper ID 1099 : 2014/2
CHARACTERISTICS OF ALMOST HERMITIAN MANIFOLDS WITH VANISHING BOCHNER CURVATURE TENSOR
Ognian Kassabov It is known that a Riemannian manifold of dimension n>3 is conformal flat if and only if its Weil curvature tensor vanishes identically. The Bochner curvature tensor for a Kähler manifold is defined as a formal analogue of the Weil’s one. Hence it is important to know its geometric characteristics. In this paper we find such characteristics for the generalization of the Bochner tensor for an arbitrary almost Hermitian manifold.
Почти Ермитови многообразия тензор на Бохнер секционна кривина.Almost Hermitian manifolds Bochner curvature tensor sectional curvature.Ognian Kassabov BIBLIOGRAPHY [1] G. Stanilov: Doktorska disertatsiya. Sofiya, 1977. ( [1] Г. Станилов: Докторска дисертация. София, 1977. ) [2] S. Bochner: Curvature and Betti numbers II. Ann. of Math. 50(1949), 77-93. [3] G. Ganchev: Characteristic of some classes of almost Hermitian manifolds. SerdicaMath. J., 4(1978), 19-23. [4] G. Ganchev: Almost Hermitian manifolds similar to the complex space forms.C. R. Acad. Bulgare Sci., 32(1979), 1179-1182. [5] G. Ganchev: Conformal type and Bochner tensors for almost Hermitian manifolds. C. R. Acad. Bulgare Sci., 34(1981), 1065-1068. [6] G. Ganchev: On Bochner curvature tensors in almost Hermitian manifolds. Pliska Stud. Math. Bulgar., 9(1987), 33-43. [7] R. S. Kulkarni: Curvature structure and conformal transformations. Bull. Amer. Math. Soc., 75(1969), 91-94. [8] J. A. Schouten: Ricci-calculus. Springer-Verlag, Berlinand New York, 1954. [9] Fr. Tricerri, L. Vanhecke: Curvature tensors on almost Hermitian manifolds. Trans. Amer. Math. Soc., 267(1981), 365-398. [10] L. Vanhecke, K. Yano: Almost Hermitian manifolds and the Bochner curvature tensor. Kodai Math. Sem. Rep., 29(1977), 10-21. |
