TY - JOUR

T1 - Björling formula for mean curvature one surfaces in hyperbolic three-space and in de sitter three-space

AU - Yang, Seong-Deog

PY - 2017

Y1 - 2017

N2 - We solve the Björling problem for constant mean curvature one surfaces in hyperbolic three-space and in de Sitter three-space. That is, we show that for any regular, analytic (and spacelike in the case of de Sitter three-space) curve and an analytic (timelike in the case of de Sitter three-space) unit vector field N along and orthogonal to γ, there exists a unique (spacelike in the case of de Sitter three-space) surface of constant mean curvature 1 which contains γ and the unit normal of which on γ is N. Some of the consequences are the planar reflection principles, and a classification of rotationally invariant CMC 1 surfaces.

AB - We solve the Björling problem for constant mean curvature one surfaces in hyperbolic three-space and in de Sitter three-space. That is, we show that for any regular, analytic (and spacelike in the case of de Sitter three-space) curve and an analytic (timelike in the case of de Sitter three-space) unit vector field N along and orthogonal to γ, there exists a unique (spacelike in the case of de Sitter three-space) surface of constant mean curvature 1 which contains γ and the unit normal of which on γ is N. Some of the consequences are the planar reflection principles, and a classification of rotationally invariant CMC 1 surfaces.

KW - Björling formula

KW - Constant mean curvature surfaces

KW - De sitter space

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U2 - 10.4134/BKMS.b150984

DO - 10.4134/BKMS.b150984

M3 - Article

AN - SCOPUS:85010782658

VL - 54

SP - 159

EP - 175

JO - Bulletin of the Korean Mathematical Society

JF - Bulletin of the Korean Mathematical Society

SN - 1015-8634

IS - 1

ER -