The Spectral Geometry of Some Almost Hermitian Manifolds

Let (M i , g i ) be a certain almost Hermitian 2n-manifold M i with a Hermitian metric g i for i = 1, 2, which is more general than an almost L manifold (a Khlerian manifold is known to be a special almost L manifold).Let Spec p (M i , g i ) denote the spectrum of the real Laplacian on p-forms on M i .The purpose of this paper is to show that for some special values of p and n, if Spec p (M 1 , g 1 ) = Spec p (M 2 , g 2 ), then (M 1 , g 1 ) is of constant holomorphic sectional curvature H 1 if and only if (M 2 , g 2 ) is of constant holomorphic sectional curvature H 2 , and H 2 = H 1 .The corresponding results on almost L manifolds were obtained by C. C.