Complete classification of spatial surfaces with parallel mean curvature vector in arbitrary non-flat pseudo-Riemannian space forms

Central European Journal of Mathematics ◽

10.2478/s11533-009-0020-9 ◽

2009 ◽

Vol 7 (3) ◽

pp. 400-428 ◽

Author(s):

Bang-Yen Chen

Keyword(s):

Mean Curvature ◽

Riemannian Space ◽

Curvature Vector ◽

Complete Classification ◽

Mean Curvature Vector ◽

Parallel Mean Curvature Vector ◽

Space Forms ◽

Parallel Mean Curvature ◽

Riemannian Space Forms

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Classification of Lorentz surfaces with parallel mean curvature vector in non-flat pseudo-Riemannian space forms $S_2^4(1)$ and $H_2^4(-1)$

Bulletin of the Belgian Mathematical Society - Simon Stevin ◽

10.36045/bbms/1382448191 ◽

2013 ◽

Vol 20 (4) ◽

pp. 715-733

Author(s):

Dan Yang ◽

Yu Fu

Keyword(s):

Mean Curvature ◽

Riemannian Space ◽

Curvature Vector ◽

Mean Curvature Vector ◽

Parallel Mean Curvature Vector ◽

Space Forms ◽

Parallel Mean Curvature ◽

Riemannian Space Forms

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The classification of the surfaces with parallel mean curvature vector in two-dimensional complex space forms

American Journal of Mathematics ◽

10.1353/ajm.2000.0012 ◽

2000 ◽

Vol 122 (2) ◽

pp. 295-317 ◽

Author(s):

K. (Katsuei) Kenmotsu ◽

Detang Zhou

Keyword(s):

Mean Curvature ◽

Complex Space ◽

Curvature Vector ◽

Mean Curvature Vector ◽

Two Dimensional ◽

Parallel Mean Curvature Vector ◽

Space Forms ◽

Parallel Mean Curvature ◽

Complex Space Forms

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Correction to “The classification of the surfaces with parallel mean curvature vector in two-dimensional complex space forms”

American Journal of Mathematics ◽

10.1353/ajm.2016.0015 ◽

2016 ◽

Vol 138 (2) ◽

pp. 395-402 ◽

Author(s):

Katsuei Kenmotsu

Keyword(s):

Mean Curvature ◽

Complex Space ◽

Curvature Vector ◽

Mean Curvature Vector ◽

Two Dimensional ◽

Parallel Mean Curvature Vector ◽

Space Forms ◽

Parallel Mean Curvature ◽

Complex Space Forms

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COMPLETE CLASSIFICATION OF LORENTZ SURFACES WITH PARALLEL MEAN CURVATURE VECTOR IN ARBITRARY PSEUDO-EUCLIDEAN SPACE

Kyushu Journal of Mathematics ◽

10.2206/kyushujm.64.261 ◽

2010 ◽

Vol 64 (2) ◽

pp. 261-279 ◽

Author(s):

Bang-Yen CHEN

Keyword(s):

Euclidean Space ◽

Mean Curvature ◽

Curvature Vector ◽

Complete Classification ◽

Mean Curvature Vector ◽

Parallel Mean Curvature Vector ◽

Parallel Mean Curvature

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On complete spacelike submanifolds in semi-Riemannian space forms with parallel normalized mean curvature vector

Kodai Mathematical Journal ◽

10.2996/kmj/1301576760 ◽

2011 ◽

Vol 34 (1) ◽

pp. 42-54 ◽

Author(s):

Xiaoli Chao

Keyword(s):

Mean Curvature ◽

Riemannian Space ◽

Curvature Vector ◽

Mean Curvature Vector ◽

Space Forms ◽

Spacelike Submanifolds ◽

Riemannian Space Forms

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Biharmonic Submanifolds with Parallel Normalized Mean Curvature Vector Field in Pseudo-Riemannian Space Forms

Bulletin of the Malaysian Mathematical Sciences Society ◽

10.1007/s40840-017-0556-y ◽

2017 ◽

Vol 42 (4) ◽

pp. 1469-1484 ◽

Author(s):

Li Du ◽

Juan Zhang

Keyword(s):

Vector Field ◽

Mean Curvature ◽

Riemannian Space ◽

Curvature Vector ◽

Mean Curvature Vector ◽

Biharmonic Submanifolds ◽

Space Forms ◽

Riemannian Space Forms

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Constant Gaussian Curvature Surfaces with Parallel Mean Curvature Vector in Two-Dimensional Complex Space Forms

Geometriae Dedicata ◽

10.1007/s10711-005-9038-8 ◽

2006 ◽

Vol 118 (1) ◽

pp. 229-244 ◽

Author(s):

Shinya Hirakawa

Keyword(s):

Mean Curvature ◽

Complex Space ◽

Curvature Vector ◽

Mean Curvature Vector ◽

Two Dimensional ◽

Parallel Mean Curvature Vector ◽

Constant Gaussian Curvature ◽

Space Forms ◽

Parallel Mean Curvature ◽

Complex Space Forms

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Classification of Lorentzian surfaces with parallel mean curvature vector in % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfKttLearuqr1ngBPrgarmWu51MyVXguY9 % gCGievaerbd9wDYLwzYbWexLMBbXgBcf2CPn2qVrwzqf2zLnharyav % P1wzZbItLDhis9wBH5garqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC % 0xbbL8F4rqqrFfpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yq % aqpepae9pg0FirpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaabe % qaamaaeaqbaaGcbaWefv3ySLgznfgDOjdarCqr1ngBPrginfgDObcv % 39gaiyaacqWFecFrdaqhaaWcbaGaeGOmaidabaGaeGinaqdaaaaa!49CF! $$ \mathbb{E}_2^4 $$

Acta Mathematica Hungarica ◽

10.1007/s10474-010-9157-z ◽

2010 ◽

Vol 128 (1-2) ◽

pp. 59-81 ◽

Author(s):

Z. H. Hou ◽

D. Yang

Keyword(s):

Mean Curvature ◽

Curvature Vector ◽

Mean Curvature Vector ◽

Parallel Mean Curvature Vector ◽

Parallel Mean Curvature

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Complete spacelike submanifolds with parallel mean curvature vector in a semi-Riemannian space form

Journal of Geometry and Physics ◽

10.1016/j.geomphys.2005.11.015 ◽

2006 ◽

Vol 56 (10) ◽

pp. 2177-2188 ◽

Author(s):

A. Brasil ◽

Rosa M.B. Chaves ◽

M. Mariano

Keyword(s):

Mean Curvature ◽

Riemannian Space ◽

Curvature Vector ◽

Mean Curvature Vector ◽

Parallel Mean Curvature Vector ◽

Parallel Mean Curvature ◽

Spacelike Submanifolds

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Surfaces with parallel mean curvature vector in complex space forms

Journal of Differential Geometry ◽

10.4310/jdg/1344430822 ◽

2012 ◽

Vol 91 (2) ◽

pp. 215-232 ◽

Author(s):

Dorel Fetcu

Keyword(s):

Mean Curvature ◽

Complex Space ◽

Curvature Vector ◽

Mean Curvature Vector ◽

Parallel Mean Curvature Vector ◽

Space Forms ◽

Parallel Mean Curvature ◽

Complex Space Forms

Download Full-text