报告题目：Study of Lagrangian submanifolds of S^3*S^3 with constant angle functions

报告人：Marilena Moruz博士

时间：2017年5月8日（星期一）上午10:00—11:00

地点：数学与统计学院教学楼301教室

报告内容摘要：In the present talk, we study minimal Lagrangian submanifolds in the nearly Kaehler $S^3*S^3$ described by $g\mapto f(g) = (p(g), q(g))$ and angle functions $\theta_1,\theta_2,\theta_3$. We show that if all angle functions are constant, then the submanifold is either totally geodesic or has constant sectional curvature and thus there is a classification. Moreover, we show that if precisely one angle function is constant, then it must be equal to $0, \pi/3, 2\pi/3$. Using then two remarkable constructions, we prove that it is sufficient to study the case when $\theta_1=\pi/3, \theta_2 =\Lambda+\pi/3$ and $\theta_3 =-\Lambda+\pi/3$, where $\Lambda$ is a non constant function. It results into a special case for which $p$ is not an immersion. We show that such a minimal Lagrangian submanifold in the nearly Kaehler $S^3*S^3$ is a frame bundle over a minimal surface and is determined by a differential equation. Moreover, we study as well the reverse problem, in the cases when the surface is totally geodesic or not.

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