Tohoku Mathematical Journal
2002

June
SECOND SERIES VOL. 54, NO. 2

Tohoku Math. J.
54 (2002), 319-328

Title SOME DIFFERENTIAL GEOMETRIC PROPERTIES OF CODIMENSION-ONE FOLIATIONS OF POLYNOMIAL GROWTH

Author Gen-ichi Oshikiri

(Received July 3, 2000, revised January 16, 2001)
Abstract. We show that a codimension-one minimal foliation with growth at most 2 of a complete Riemannian manifold with non-negative Ricci curvature is totally geodesic. We present some foliated versions of the result given by Alencar and do Carmo, and of minimal graphs by Miranda. Further, we simplify the proof of Meeks' result concerning constant mean curvature foliations of 3-dimensional Euclidean space.

2000 Mathematics Subject Classification. Primary 53C12.

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