SUT J. Math. 32 (2), 163-178, (June 1996) DOI: 10.55937/sut/1262208593
Chuan-Chih Hsiung, Wenmao Yang, Bonnie Xiong
KEYWORDS: spectrum, Laplacian, almost complex structures, almost Hermitian structures, holomorphic sectional curvature, Bochner curvature tensor, 53C15, 53C35, 58G25
Let be a certain almost Hermitian -manifold with a Hermitian metric for , which is more general than an almost manifold (a Käshlerian manifold is known to be a special almost manifold). Let denote the spectrum of the real Laplacian on -forms on . The purpose of this paper is to show that for some special values of and , if , then is of constant holomorphic sectional curvature if and only if is of constant holomorphic sectional curvature , and . The corresponding results on almost manifolds were obtained by C. C. Hsiung and C. X. Wu (The spectral geometry of almost manifolds, Bull. Inst. Math. Acad. Sinica, 23 (1995), 229–241).