GENERAL SCHWARZ LEMMAS BETWEEN PSEUDO-HERMITIAN MANIFOLDS AND HERMITIAN MANIFOLDS∗

Abstract

From the viewpoint of differential geometry, Schwarz lemmas of distance-decreasing type and volume-decreasing type can be obtained by the estimates of sum functions and product functions of all eigenvalues of holo-morphic maps. This paper investigates general Schwarz lemmas by estimating partial sum functions and partial product functions of the eigenvalues of generalized holomorphic maps between pseudo-Hermitian manifolds and Hermitian manifolds.