On Lagrangian submanifolds of the nearly Kaehler 6-Sphere

Journal Article

Deshmukh, Ramesh Sharma and Sharief . 2016

• Publication Work Type: Research Article
• Publication Online URL: On Lagrangian submanifolds of the nearly Kaehler 6-Sphere
• Magazine \ Newspaper: American Mathematical Society in the collection Contemporary Mathematics
• Volume Number: 674
• Pages: 153-160

Publication Abstract

Recalling the recent results obtained by Sharma, Deshmukh and
Al-Solamy [SD] for a canonically induced almost contact metric structure by
a global unit tangent vector field on a Lagrangian submanifold of the nearly
Kaehler 6-sphere, we show that, if this canonical almost metric structure is nearly Sasakian (respectively, nearly cosymplectic), then it reduces to Sasakian (respectively, cosymplectic). Next we show that, if the normal connection of a Lagrangian submanifold M of the nearly Kaehler S6 is flat, then M is the totally geodesic S3. Finally, we present a generalization of a result of Ejiri and obtain a condition for a 3-dimensional submanifold of the nearly Kaehler S6
to be Lagrangian.