CR submanifolds in a sphere and their Gauss maps 被引量：1

CR submanifolds in a sphere and their Gauss maps

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摘要 The relationship between CR submanifolds in a sphere and their Gauss maps are investigated.Let V be the image of a sphere by a rational holomorphic map F with degree two in another sphere.It is show that the Gauss map of V is degenerate if and only if F is linear fractional. The relationship between CR submanifolds in a sphere and their Gauss maps are investigated. Let V be the image of a sphere by a rational holomorphic map F with degree two in another sphere. It is show that the Gauss map of V is degenerate if and only if F is linear fractional.

作者 CHENG XiaoLiang JI ShanYu LIU WeiMing

机构地区 Department of Mathematics Department of Mathematics Department of Mathematics Department of Mathematics and Physics

出处《Science China Mathematics》 SCIE 2013年第5期1041-1049,共9页 中国科学：数学（英文版）

关键词 CR submanifold Gauss maps CR子流形高斯映射球体全纯映射分数

分类号 O186.12 [理学—基础数学]

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参考文献2

1CHEN Zhihua, Jl Shanyu & XU Dekang Department of Mathematics, Tongji University, Shanghai 200092, China,Department of Mathematics, University of Houston, Houston, TX 77204, USA.Rational holomorphic maps from B^2 into B^N with degree 2[J].Science China Mathematics,2006,49(11):1504-1522. 被引量：3
2JI ShanYu 1 & ZHANG Yuan 2 1 Department of Mathematics, University of Houston, Houston, TX 77204, USA 2 Department of Mathematics, University of California at San Diego, La Jolla, CA 92093, USA.Classification of rational holomorphic maps from B^2 into B^N with degree 2[J].Science China Mathematics,2009,52(12):2647-2667. 被引量：5

二级参考文献17

1CHEN Zhihua, Jl Shanyu & XU Dekang Department of Mathematics, Tongji University, Shanghai 200092, China,Department of Mathematics, University of Houston, Houston, TX 77204, USA.Rational holomorphic maps from B^2 into B^N with degree 2[J].Science China Mathematics,2006,49(11):1504-1522. 被引量：3
2[1]Faran J.Maps from the two ball to the three ball.Invent Math,1982,68:441-475
3[2]D'Angelo J P.Proper holomorphic mappings between balls of different dimensions.Mich Math J,1988,35:83-90
4[3]Wono S B.Proper holomorphic mappings in Several Complex Variables.P D thesis.Urbana-Champaign:University of Illinois,1993
5[4]Huang X.On a linearity problem of proper holomorphic mappings between balls in complex spaces of different dimensions.J of Diff Geom,1999,51(1):13-33
6[5]Huang X.On a semi-rigidity property for holomorphic maps.Asian J Math,2003,7:463-492
7[6]Ji S,Xu D.Rational maps between Bn and BN with geometric rank κ0 ≤ n-2 and minimal target dimension.Asian J Math,2004,8:233-258
8[7]Huang X,Ji S,Xu D.Several results for holomorphic mappings from Bn into BN.Contemporay Math (A special issue in honor of Professor F.Treves),2005,368:267-292
9[8]Huang X,Ji S,Xu D.A new gap phenomemon for proper mapping from Bn into BN.Math Research Letter,2006,4:515-529
10[1]In the sense that if F* = T o F o σ,where both F and F* satisfy the normalized condition in Lemma 2.3,T ∈ Aut0((θ)H5) and σ ∈ Aut0((θ)H2),then F* = F

共引文献5

1JI ShanYu 1 & ZHANG Yuan 2 1 Department of Mathematics, University of Houston, Houston, TX 77204, USA 2 Department of Mathematics, University of California at San Diego, La Jolla, CA 92093, USA.Classification of rational holomorphic maps from B^2 into B^N with degree 2[J].Science China Mathematics,2009,52(12):2647-2667. 被引量：5
2程晓亮.B^2到B^4上的一族逆紧全纯多项式映照[J].吉林师范大学学报（自然科学版）,2014,35(2):49-51. 被引量：5
3程晓亮,王博.B^(2)到B^(5)的4次逆紧全纯单项式映照[J].吉林师范大学学报（自然科学版）,2021,42(2):58-62. 被引量：2
4彭勃,王丽欣.B^(2)到B^(9)的某类5次逆紧全纯映照[J].数学学习与研究,2021(35):137-139.
5程晓亮,郭长聪.B^(2)到B^(10)的某类7次逆紧全纯映射[J].吉林师范大学学报（自然科学版）,2024,45(2):45-49.

同被引文献1

1JI ShanYu 1 & ZHANG Yuan 2 1 Department of Mathematics, University of Houston, Houston, TX 77204, USA 2 Department of Mathematics, University of California at San Diego, La Jolla, CA 92093, USA.Classification of rational holomorphic maps from B^2 into B^N with degree 2[J].Science China Mathematics,2009,52(12):2647-2667. 被引量：5

引证文献1

1程晓亮.B^2到B^4上的一族逆紧全纯多项式映照[J].吉林师范大学学报（自然科学版）,2014,35(2):49-51. 被引量：5

二级引证文献5

1程晓亮,刘阳,迟明月,孙爱慧.C^n中单位球间逆紧全纯映射的构造[J].吉林师范大学学报（自然科学版）,2019,40(1):66-71. 被引量：1
2程晓亮,王博.B^(2)到B^(5)的4次逆紧全纯单项式映照[J].吉林师范大学学报（自然科学版）,2021,42(2):58-62. 被引量：2
3王博.单复变与多复变的几点比较[J].产业与科技论坛,2021,20(14):50-52. 被引量：1
4董欣,马会波.B^(3)到B^(16)的一类逆紧全纯式[J].数学学习与研究,2022(8):143-145. 被引量：1
5程晓亮,郭长聪.B^(2)到B^(10)的某类7次逆紧全纯映射[J].吉林师范大学学报（自然科学版）,2024,45(2):45-49.

1王秀荣,吴报强.四元数射影空间的generic子流形[J].徐州师范大学学报（自然科学版）,2005,23(2):30-34.
2张则增,王宗贵.近乎Sasakian流形的CR子流形[J].Chinese Quarterly Journal of Mathematics,2000,15(1):84-87.
3梁希泉,刘西民.Bochner－Kaehler流形的CR子流形[J].东北师大学报（自然科学版）,1994,26(4):6-9.
4许志才,徐森林.CR-submanifolds in Almost Hermitian Manifold[J].Chinese Quarterly Journal of Mathematics,2001,16(3):1-7.
5刘西民.P-SASAKIAN流形的CR子流形(英文)[J].南开大学学报（自然科学版）,1997,30(4):26-30.
6东瑜昕.复射影空间中的CR-子流形[J].数学学报（中文版）,1993,36(3):321-334. 被引量：6
7KONG LingLing,PEI DongHe.Singularities of de Sitter Gauss map of timelike hypersurface in Minkowski 4-space[J].Science China Mathematics,2008,51(2):241-249. 被引量：9
8许志才,李海中.殆Hermitian流形中的CR子流形[J].淮南矿业学院学报,1991,11(3):112-118.
9韩拥军.关于复射影空间中若干子流形问题的研究[J].铜陵职业技术学院学报,2012,11(2):67-69.
10张则增.切触Bochner-Kenmotsu流形的CR子流形[J].山东师范大学学报（自然科学版）,2000,15(4):387-390.

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