Equivariant totally real 3-spheres in the complex projective space C{double-struck}P{double-struck} n

Jie Fei; Chiakuei Peng; Xiaowei Xu

doi:10.1016/j.difgeo.2012.04.002

Equivariant totally real 3-spheres in the complex projective space C{double-struck}P{double-struck} ⁿ

Jie Fei
, Chiakuei Peng
, Xiaowei Xu^*

^*Corresponding author for this work

Xi'an Jiaotong-Liverpool University
University of Science and Technology of China

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

In this paper we study the equivariant totally real immersions from S ³ into C{double-struck}P{double-struck} ⁿ. We first reduce these immersions to a system of algebraic equations by the unitary representations of SU(2). We give some explicit examples of minimal totally real isometric immersions from S3/m(m+2)3 into C{double-struck}P{double-struck} ⁿ, and characterize the minimal totally real isometric immersions from S3/m(m+2)3 into C{double-struck}P{double-struck} ⁿ by the standard example. We also give many minimal linearly full isometric immersions from S1/53 into C{double-struck}P{double-struck} ⁷, C{double-struck}P{double-struck} ¹¹ and C{double-struck}P{double-struck} ¹⁵. As an application of our method, we classify equivariant Lagrangian S ³ in C{double-struck}P{double-struck} ³ again.

Original language	English
Pages (from-to)	262-273
Number of pages	12
Journal	Differential Geometry and its Application
Volume	30
Issue number	3
DOIs	https://doi.org/10.1016/j.difgeo.2012.04.002
Publication status	Published - Jun 2012

Keywords

Constant sectional curvature
Equivariant totally real immersions
Lagrangian submanifolds

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10.1016/j.difgeo.2012.04.002

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@article{bc1adc26940541f3a8347a109c47161a,

title = "Equivariant totally real 3-spheres in the complex projective space C\{double-struck\}P\{double-struck\} n ",

abstract = "In this paper we study the equivariant totally real immersions from S 3 into C\{double-struck\}P\{double-struck\} n. We first reduce these immersions to a system of algebraic equations by the unitary representations of SU(2). We give some explicit examples of minimal totally real isometric immersions from S3/m(m+2)3 into C\{double-struck\}P\{double-struck\} n, and characterize the minimal totally real isometric immersions from S3/m(m+2)3 into C\{double-struck\}P\{double-struck\} n by the standard example. We also give many minimal linearly full isometric immersions from S1/53 into C\{double-struck\}P\{double-struck\} 7, C\{double-struck\}P\{double-struck\} 11 and C\{double-struck\}P\{double-struck\} 15. As an application of our method, we classify equivariant Lagrangian S 3 in C\{double-struck\}P\{double-struck\} 3 again.",

keywords = "Constant sectional curvature, Equivariant totally real immersions, Lagrangian submanifolds",

author = "Jie Fei and Chiakuei Peng and Xiaowei Xu",

note = "Funding Information: This project is supported by the NSFC (Grant Nos. 11071249 , 11101389 ), the Fundamental Research Funds for the Central Universities (USTC) and Anhui Provincial Natural Science Foundation (No. 1208085MA01 ). The authors would like to thank the refereeʼs comments. ",

year = "2012",

month = jun,

doi = "10.1016/j.difgeo.2012.04.002",

language = "English",

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pages = "262--273",

journal = "Differential Geometry and its Application",

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AU - Fei, Jie

AU - Peng, Chiakuei

AU - Xu, Xiaowei

N1 - Funding Information: This project is supported by the NSFC (Grant Nos. 11071249 , 11101389 ), the Fundamental Research Funds for the Central Universities (USTC) and Anhui Provincial Natural Science Foundation (No. 1208085MA01 ). The authors would like to thank the refereeʼs comments.

PY - 2012/6

Y1 - 2012/6

N2 - In this paper we study the equivariant totally real immersions from S 3 into C{double-struck}P{double-struck} n. We first reduce these immersions to a system of algebraic equations by the unitary representations of SU(2). We give some explicit examples of minimal totally real isometric immersions from S3/m(m+2)3 into C{double-struck}P{double-struck} n, and characterize the minimal totally real isometric immersions from S3/m(m+2)3 into C{double-struck}P{double-struck} n by the standard example. We also give many minimal linearly full isometric immersions from S1/53 into C{double-struck}P{double-struck} 7, C{double-struck}P{double-struck} 11 and C{double-struck}P{double-struck} 15. As an application of our method, we classify equivariant Lagrangian S 3 in C{double-struck}P{double-struck} 3 again.

AB - In this paper we study the equivariant totally real immersions from S 3 into C{double-struck}P{double-struck} n. We first reduce these immersions to a system of algebraic equations by the unitary representations of SU(2). We give some explicit examples of minimal totally real isometric immersions from S3/m(m+2)3 into C{double-struck}P{double-struck} n, and characterize the minimal totally real isometric immersions from S3/m(m+2)3 into C{double-struck}P{double-struck} n by the standard example. We also give many minimal linearly full isometric immersions from S1/53 into C{double-struck}P{double-struck} 7, C{double-struck}P{double-struck} 11 and C{double-struck}P{double-struck} 15. As an application of our method, we classify equivariant Lagrangian S 3 in C{double-struck}P{double-struck} 3 again.

KW - Constant sectional curvature

KW - Equivariant totally real immersions

KW - Lagrangian submanifolds

UR - https://www.scopus.com/pages/publications/84859754022

U2 - 10.1016/j.difgeo.2012.04.002

DO - 10.1016/j.difgeo.2012.04.002

M3 - Article

AN - SCOPUS:84859754022

SN - 0926-2245

VL - 30

SP - 262

EP - 273

JO - Differential Geometry and its Application

JF - Differential Geometry and its Application

IS - 3

ER -

Equivariant totally real 3-spheres in the complex projective space C{double-struck}P{double-struck} ⁿ

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