Acta mathematica scientia,Series A ›› 2016, Vol. 36 ›› Issue (6): 1027-1039.

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Surfaces in Products of Semi-Riemannian Space Forms with Parallel Mean Curvature Vector

Qiu Wanghua1, Hou Zhonghua2   

  1. 1. College of Sciences, Jiujiang University, Jiangxi Jiujiang 332005;
    2. Institute of Mathematics, Dalian University of Technology, Liaoning Dalian 116024
  • Received:2016-02-24 Revised:2016-07-31 Online:2016-12-26 Published:2016-12-26
  • Supported by:

    Supported by the NSFC (61473059)

Abstract:

Batista introduced a special (1,1) tensor S on a CMC immersed surface Σ2 in M2(c)×R. Later on, Fetcu and Rosebberg extended (1,1) tensor S to PMC surface Σ2Mn-1(c)×R. In the present paper, the authors consider a more general tensor S on PMC immersed surface Σ2 in Lorentzian product spaces (Mn-1(c)×R, g-1) and Riemmannian product spaces (Mn-1(c)×R, g+1). The authors compute the Simons type equations of |S|2, and characterize CMC surfaces in (M2(c)×R, gε). For case ε=+1, we obtain several pinching constants greater than that given by Batista.

Key words: Parallel mean curvature vector, Simons type equation, Product spaces, Pinching constants

CLC Number: 

  • O186.12
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