Almost Contact Lagrangian Submanifolds of Nearly Kaehler 6-Sphere

作者：Sharma Ramesh^*; Deshmukh Sharief; Al Solamy Falleh

来源：Results in Mathematics, 2014, 65(1-2): 143-153.

DOI：10.1007/s00025-013-0335-5

• Nearly Kaehler unit 6-sphere
• Lagrangian submanifold
• contact metric structure
• Sasakian structure
• cosymplectic structure

For a Lagrangian submanifold M of S-6 with nearly Kaehler structure, we provide conditions for a canonically induced almost contact metric structure on M by a unit vector field, to be Sasakian. Assuming M contact metric, we show that it is Sasakian if and only if the second fundamental form annihilates the Reeb vector field xi, furthermore, if the Sasakian submanifold M is parallel along xi, then it is the totally geodesic 3-sphere. We conclude with a condition that reduces the normal canonical almost contact metric structure on M to Sasakian or cosymplectic structure.

• 出版日期2014-2