Fullness and scalar curvature of the totally real submanifolds in ![S<sup>6</sup>(1)](http://siba-ese.unile.it/plugins/generic/latexRender/cache/8b585d742a20aa88a374f7c8026084ab.png)
Abstract
Let M be a totally rea1 3-dimensional submanifold of the nearly Kähler 6-sphere
. 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
, then M is full in
unless M is totally geodesic. A family of examples with
, which are fully contained in some great hypersphere
, are also defined in an explicit manner.
![S<sup>6</sup>(1)](http://siba-ese.unile.it/plugins/generic/latexRender/cache/8b585d742a20aa88a374f7c8026084ab.png)
![R≠ 2](http://siba-ese.unile.it/plugins/generic/latexRender/cache/683f28d0212556681543e2c04789cc1f.png)
![S<sup>6</sup>( 1)](http://siba-ese.unile.it/plugins/generic/latexRender/cache/229b2bb4b0f43ea7f962272a3f920e4e.png)
![R≡ 2](http://siba-ese.unile.it/plugins/generic/latexRender/cache/2e0542f769aaa40b7bc7c261a6f212c2.png)
![S<sup>5</sup>( 1)⊂ S<sup>6</sup>(1)](http://siba-ese.unile.it/plugins/generic/latexRender/cache/dccfad7044c9c63af1cae68523239b36.png)
DOI Code:
10.1285/i15900932v16n1p105
Keywords:
Fullness scalar curvature; Totally real submanifolds; Nearly Kähler structure; Minimality
Classification:
53C42
Full Text: PDF