Orbits of rank one and parallel mean curvature

Author:
Carlos Olmos

Journal:
Trans. Amer. Math. Soc. **347** (1995), 2927-2939

MSC:
Primary 53C30; Secondary 53C42

DOI:
https://doi.org/10.1090/S0002-9947-1995-1308018-4

MathSciNet review:
1308018

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Abstract: Let be a (extrinsic) homogeneous irreducible full submanifold of Euclidean space with (i.e., it admits locally defined, linearly independent parallel normal vector fields). We prove that must be contained in a sphere. This result toghether with previous work of the author about homogeneous submanifolds of higher rank imply, in particular, the following theorem: A homogeneous irreducible submanifold of Euclidean space with parallel mean curvature vector is either minimal, or minimal in a sphere, or an orbit of the isotropy representation of a simple symmetric space.

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DOI:
https://doi.org/10.1090/S0002-9947-1995-1308018-4

Article copyright:
© Copyright 1995
American Mathematical Society