Schouten Bracket of Holomorphic Tensors of a Kahlerian Manifold
Abstract
Abstract. It is shown that the Schouten bracket of holomorphic tensors of a compact kahlerian manifold W defines a structure of graded complex Lie algebra on the space of holomorphic tensors of the manifold. We obtain an important proposition which generalizes a wellknown result of Lichnerowicz [6,7].
Ringkasan. Kita perlihatkan bahwa "Schouten bracket" dari pada tensor-tensot holomorph milik suatu manifold kahler yang kompak W mendefinisikan suatu struktur "graded complex Lie algebra" pada ruang tensor-tenso holomorph dari pada manifold tersebut. Disini diperoleh suatu proposisi yang penting yang memperluas sebuah hasil yang terkenal dari Lichnerowicz [6,7].
References
Bochner, S. and Montgomery, D.: Group of differentiable and real or complex transformations, Ann. of Math, 46 (1945) , 689-694.
Ibrahim, J.: These de Doctorat d'Etat Sci. Univ. de Paris, (1974).
Ibrahim, J. et Lichnerowicz, A.: Tenseurs holomorphes sur une variete kahlerienne compacte, C.R.Acad. Sci. Paris, 277 (1973) Ser. A., 801-806.
Kobayashi, S.: Transformation group in differential geometry. Spr. VerI. 1972, Ch. III.
Lichnerowicz, A.: Sur certaines varietes kahleriennes compactes, C.R.Acad. Sci. Paris, 263 (1966), Ser. A. 570-575.
Lichnerowicz, A.: Varietes kahleriennes et premiere classe de Chern, J. of Diff. Geom., 1 (1967), 195-224.
Lichnerowicz, A.: Varietes kahleriennes a premiere classe de Chern non negative et varietes riemanniennes a courbure de Ricci generalisee non negative, J. of Diff. Geom., 6 (1971), 47-94.
Nijenhuis, A.: Indag. Math. 17, 1955, 390-403.
Schouten, J.A.: Conv. Int. Geom. Diff., Ed. Cremonese Roma 1954.
