Title: On J-parallel totally real three-dimensional submanifolds of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:msup><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mn>6</mml:mn></mml:mrow></mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>
Abstract: In this paper, we study totally real submanifolds of the nearly Kähler six-dimensional unit sphere. Since in this case also, parallel submanifolds are totally geodesic, we introduce a weaker condition, namely that for any tangent vector v〈(∇h)(v,v,v),Jv〉=0. We obtain a complete classification of totally real three-dimensional submanifolds of S6(1) satisfying the above condition.