Schwarz Lemma for VT harmonic map

Abstract

In this paper, we obtained Schwarz Lemma of $ VT $ harmonic map including distance decreasing property and volume decreasing property under some conditions about the eigenvalue of $ du^{+} \circ du $, $ T $ and the lower bound of $ Ric_f^N $ or $ Ric_V^N $. We generalized Schwarz lemma of $ V $ harmonic map.