This article is cited in 5 papers

On the Constant Type of Almost Hermitian Manifolds

V. F. Kirichenko, I. V. Tret'yakova

Moscow State Pedagogical University

Abstract: We suggest a most natural generalization of the notion of constant type for nearly Kählerian manifolds introduced by A. Gray to arbitrary almost Hermitian manifolds. We prove that the class of almost Hermitian manifolds of zero constant type coincides with the class of Hermitian manifolds. We show that the class of $G_1$-manifolds of zero constant type coincides with the class of 6-dimensional $G_1$-manifolds with a non-integrable structure. Finally, we prove that the class of normal $G_2$-manifolds of nonzero constant type coincides with the class of 4-dimensional $G_2$-manifolds with a nonintegrable structure.

UDC: 517

Received: 02.02.2000

DOI: 10.4213/mzm988

 English version: Mathematical Notes, 2000, 68:5, 569–575

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