Schwarz-type lemmas for generalized holomorphic maps between pseudo-Hermitian manifolds and Hermitian manifolds

被引：5

作者：

Chong, Tian ^{[1
]}

Dong, Yuxin ^{[2
]}

Ren, Yibin ^{[3
]}

Yu, Weike ^{[2
]}

机构：

[1] Shanghai Polytech Univ, Coll Arts & Sci, Sch Sci, 2360 Jin Hai Rd, Shanghai 201209, Peoples R China

[2] Fudan Univ, Sch Math Sci, 220 Handan Rd, Shanghai 200433, Peoples R China

[3] Zhejiang Normal Univ, Coll Math & Comp Sci, 688 Yingbin Rd, Jinhua 321004, Zhejiang, Peoples R China

来源：

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | 2021年 / 53卷 / 01期

关键词：

53C25 (primary); 32V20 (secondary);

D O I：

10.1112/blms.12394

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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, the Liouville theorem and little Picard theorem for basic CR functions are deduced. Finally, we study CR Caratheodory pseudo-distance on CR manifolds.

引用

页码：26 / 41

页数：16

共 20 条

[1] An extension of Schwarz's lemma
Ahlfors, Lars V.
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1938, 43 (1-3) : 359 - 364
[2] [Anonymous], 1968, Journal of Differential Geometry
[3] Boyer C., 2008, Sasakian Geometry
[4] The black lemma in analytical functions of two complex quantitative characteristics
Caratheodory, C
[J]. MATHEMATISCHE ANNALEN, 1927, 97 : 76 - 98
[5] CHEN Z, 1979, SCI SINICA, V22, P1238
[6] Chern S.-s., 1968, P S PURE MATH, V11, P157
[7] Pseudo-harmonic Maps from Complete Noncompact Pseudo-Hermitian Manifolds to Regular Balls
Chong, Tian
Dong, Yuxin
Ren, Yibin
Zhang, Wei
[J]. JOURNAL OF GEOMETRIC ANALYSIS, 2020, 30 (04) : 3512 - 3541
[8] ON HARMONIC AND PSEUDOHARMONIC MAPS FROM PSEUDO-HERMITIAN MANIFOLDS
Chong, Tian
Dong, Yuxin
Ren, Yibin
Yang, Guilin
[J]. NAGOYA MATHEMATICAL JOURNAL, 2019, 234 : 170 - 210
[9] Chow W-L., 1939, Math. Ann, V117, P98, DOI [10.1007/BF01450011, DOI 10.1007/BF01450011]
[10] Schwarz Type Lemmas for Pseudo-Hermitian Manifolds
Dong, Yuxin
Ren, Yibin
Yu, Weike
[J]. JOURNAL OF GEOMETRIC ANALYSIS, 2021, 31 (03) : 3161 - 3195

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