Fullness and scalar curvature of the totally real submanifolds in S<sup>6</sup>(1)


Let M be a totally rea1 3-dimensional submanifold of the nearly Kähler 6-sphere S<sup>6</sup>(1). Theorems are proven on the relation between the fullness and the scalar curvature R of M. In particular, if either R is a constant different from 2, or M is compact with R≠ 2, then M is full in S<sup>6</sup>( 1) unless M is totally geodesic. A family of examples with R≡ 2, which are fully contained in some great hypersphere S<sup>5</sup>( 1)⊂ S<sup>6</sup>(1), are also defined in an explicit manner.

DOI Code: 10.1285/i15900932v16n1p105

Keywords: Fullness scalar curvature; Totally real submanifolds; Nearly Kähler structure; Minimality

Classification: 53C42

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