Conformal homogeneous spacelike surfaces in 3-dimensional Lorentz space forms

Xiu Ji; Tongzhu Li

doi:10.1016/j.difgeo.2020.101667

Conformal homogeneous spacelike surfaces in 3-dimensional Lorentz space forms

Xiu Ji, Tongzhu Li^*

^*Corresponding author for this work

School of Mathematics and Statistics

Beijing Institute of Technology

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

Abstract

Let M₁³(c) be an 3-dimensional Lorentz space form and C(M₁³(c)) denote the conformal transformation group of M₁³(c). A spacelike surface x:M²→M₁³(c) is called a conformal homogeneous spacelike surface. If there exists a subgroup G⊂C(M₁³(c)) such that the orbit G(p)=x(M²),p∈x(M²). In this paper, we classify completely conformal homogeneous spacelike surfaces up to a conformal transformation of M₁³(c).

Original language	English
Article number	101667
Journal	Differential Geometry and its Application
Volume	73
DOIs	https://doi.org/10.1016/j.difgeo.2020.101667
Publication status	Published - Dec 2020

Keywords

Conformal homogeneous spacelike surface conformal transformation group
Conformal invariants
Homogeneous spacelike surface

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10.1016/j.difgeo.2020.101667

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abstract = "Let M13(c) be an 3-dimensional Lorentz space form and C(M13(c)) denote the conformal transformation group of M13(c). A spacelike surface x:M2→M13(c) is called a conformal homogeneous spacelike surface. If there exists a subgroup G⊂C(M13(c)) such that the orbit G(p)=x(M2),p∈x(M2). In this paper, we classify completely conformal homogeneous spacelike surfaces up to a conformal transformation of M13(c).",

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AU - Li, Tongzhu

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N2 - Let M13(c) be an 3-dimensional Lorentz space form and C(M13(c)) denote the conformal transformation group of M13(c). A spacelike surface x:M2→M13(c) is called a conformal homogeneous spacelike surface. If there exists a subgroup G⊂C(M13(c)) such that the orbit G(p)=x(M2),p∈x(M2). In this paper, we classify completely conformal homogeneous spacelike surfaces up to a conformal transformation of M13(c).

AB - Let M13(c) be an 3-dimensional Lorentz space form and C(M13(c)) denote the conformal transformation group of M13(c). A spacelike surface x:M2→M13(c) is called a conformal homogeneous spacelike surface. If there exists a subgroup G⊂C(M13(c)) such that the orbit G(p)=x(M2),p∈x(M2). In this paper, we classify completely conformal homogeneous spacelike surfaces up to a conformal transformation of M13(c).

KW - Conformal homogeneous spacelike surface conformal transformation group

KW - Conformal invariants

KW - Homogeneous spacelike surface

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JO - Differential Geometry and its Application

JF - Differential Geometry and its Application

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ER -

Conformal homogeneous spacelike surfaces in 3-dimensional Lorentz space forms

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Keywords

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