Fullness and scalar curvature of the totally real submanifolds in

doi:10.1285/i15900932v16n1p105

Fullness and scalar curvature of the totally real submanifolds in $S6(1)$

Li Xingxiao

Abstract

Let M be a totally rea1 3-dimensional submanifold of the nearly Kähler 6-sphere $S6(1)$ . 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 $S6( 1)$ unless M is totally geodesic. A family of examples with $R≡ 2$ , which are fully contained in some great hypersphere $S5( 1)⊂ S6(1)$ , 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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Note di Matematica

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

Abstract

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