Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms

Xiang Ma; Peng Wang

doi:10.1007/s11425-008-0052-9

Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms

Xiang Ma
, Peng Wang

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

13 Scopus citations

Abstract

Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms, a topic in Lorentzian conformal geometry which parallels the theory of Willmore surfaces in S ⁴, are studied in this paper. We define two kinds of transforms for such a surface, which produce the so-called left/right polar surfaces and the adjoint surfaces. These new surfaces are again conformal Willmore surfaces. For them the interesting duality theorem holds. As an application spacelike Willmore 2-spheres are classified. Finally we construct a family of homogeneous spacelike Willmore tori.

Original language	English
Pages (from-to)	1561-1576
Number of pages	16
Journal	Science in China, Series A: Mathematics
Volume	51
Issue number	9
DOIs	https://doi.org/10.1007/s11425-008-0052-9
State	Published - Sep 2008
Externally published	Yes

Keywords

Adjoint transforms
Duality theorem
Polar surfaces
Spacelike Willmore surfaces
Willmore 2-spheres

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10.1007/s11425-008-0052-9

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title = "Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms",

abstract = "Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms, a topic in Lorentzian conformal geometry which parallels the theory of Willmore surfaces in S 4, are studied in this paper. We define two kinds of transforms for such a surface, which produce the so-called left/right polar surfaces and the adjoint surfaces. These new surfaces are again conformal Willmore surfaces. For them the interesting duality theorem holds. As an application spacelike Willmore 2-spheres are classified. Finally we construct a family of homogeneous spacelike Willmore tori.",

keywords = "Adjoint transforms, Duality theorem, Polar surfaces, Spacelike Willmore surfaces, Willmore 2-spheres",

author = "Xiang Ma and Peng Wang",

note = "Funding Information: Received July 17, 2007; accepted December 23, 2007 DOI: 10.1007/s11425-008-0052-9 † Corresponding author This work was supported by the National Natural Science Foundation of China (Grant No.",

year = "2008",

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doi = "10.1007/s11425-008-0052-9",

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T1 - Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms

AU - Ma, Xiang

AU - Wang, Peng

N1 - Funding Information: Received July 17, 2007; accepted December 23, 2007 DOI: 10.1007/s11425-008-0052-9 † Corresponding author This work was supported by the National Natural Science Foundation of China (Grant No.

PY - 2008/9

Y1 - 2008/9

N2 - Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms, a topic in Lorentzian conformal geometry which parallels the theory of Willmore surfaces in S 4, are studied in this paper. We define two kinds of transforms for such a surface, which produce the so-called left/right polar surfaces and the adjoint surfaces. These new surfaces are again conformal Willmore surfaces. For them the interesting duality theorem holds. As an application spacelike Willmore 2-spheres are classified. Finally we construct a family of homogeneous spacelike Willmore tori.

AB - Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms, a topic in Lorentzian conformal geometry which parallels the theory of Willmore surfaces in S 4, are studied in this paper. We define two kinds of transforms for such a surface, which produce the so-called left/right polar surfaces and the adjoint surfaces. These new surfaces are again conformal Willmore surfaces. For them the interesting duality theorem holds. As an application spacelike Willmore 2-spheres are classified. Finally we construct a family of homogeneous spacelike Willmore tori.

KW - Adjoint transforms

KW - Duality theorem

KW - Polar surfaces

KW - Spacelike Willmore surfaces

KW - Willmore 2-spheres

UR - https://www.scopus.com/pages/publications/49149114644

U2 - 10.1007/s11425-008-0052-9

DO - 10.1007/s11425-008-0052-9

M3 - Article

AN - SCOPUS:49149114644

SN - 1006-9283

VL - 51

SP - 1561

EP - 1576

JO - Science in China, Series A: Mathematics

JF - Science in China, Series A: Mathematics

IS - 9

ER -

Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms

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Keywords

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