In this paper, we consider some generalized holomorphic maps between pseudo-Hermitian manifolds and Hermitian manifolds. By Bochner formulas and comparison theorems, we establish related Schwarz type results. As corollaries, Liouville theorem and lit
tle Picard theorem for basic CR functions are deduced. Finally, we study CR Caratheodory pseudodistance on CR manifolds.
In this paper, we give an estimate of sub-Laplacian of Riemannian distance functions in pseudo-Hermitian geometry which plays a similar role as Laplacian comparison theorem in Riemannian geometry, and deduce a prior horizontal gradient estimate of ps
eudo-harmonic maps from pseudo-Hermitian manifolds to regular balls of Riemannian manifolds. As an application, Liouville theorem is established under the conditions of nonnegative pseudo-Hermitian Ricci curvature and vanishing pseudo-Hermitian torsion. Moreover, we obtain the existence of pseudo-harmonic maps from complete noncompact pseudo-Hermitian manifolds to regular balls of Riemannian manifolds.
In this paper, we give some rigidity results for both harmonic and pseudoharmonic maps from CR manifolds into Riemannian manifolds or Ku007fahler manifolds. Some basicity, pluriharmonicity and Siu-Sampson type results are established for both harmonic maps and pseudoharmonic maps.
We derive some elliptic differential inequalities from the Weitzenbock formulas for the traceless Ricci tensor of a Kahler manifold with constant scalar curvature and the Bochner tensor of a Kahler-Einstein manifold respectively. Using elliptic estim
ates and maximum principle, some $L^p$ and $L^infty $ pinching results are established to characterize Kahler-Einstein manifolds among Kahler manifolds with constant scalar curvature, and others are given to characterize complex space forms among Kahler-Einstein manifolds. Finally, these pinching results may be combined to characterize complex space forms among Kahler manifolds with constant scalar curvature.
In this paper, we derive the second variation formula of pseudoharmonic maps into any pseudo-Hermitian manifolds. When the target manifold is an isometric embedded CR manifold in complex Euclidean space or a pseudo-Hermitian immersed submanifold in H
eisenberg group, we give some conditions on Weingarten maps to obtain some unstability of pseudoharmonic maps between these pseudo-Hermitian manifolds.
