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A Möbius characterization of submanifolds in real space forms with parallel mean curvature and constant scalar curvature. (English) Zbl 1088.53008
The authors provide a Möbius geometric characterization of submanifolds with parallel mean curvature vector field and constant scalar curvature in space forms in terms of the Möbius invariants for submanifolds introduced by C. P. Wang [Manuscr. Math. 96, 517–534 (1998; Zbl 0912.53012)]. Note that the space form geometries naturally appear as subgeometries of Möbius geometry.
In this way the authors generalize earlier theorems by H. L. Liu, C. P. Wang and G. S. Zhao [Tohoku Math. J. 53, 553–569 (2001; Zbl 1014.53010)] and by H. Li and C. P. Wang [Manuscr. Math. 112, 1–13 (2003; Zbl 1041.53008)].

##### MSC:
 53B25 Local submanifolds
##### Keywords:
parallel mean curvature; constant scalar curvature
Full Text:
##### References:
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