H-umbilical Lagrangian submanifolds of the nearly Kähler \mathbbS³×\mathbbS³

2020/07/27 by Antić, Miroslava, Moruz, Marilena, Van der Veken, Joeri
#53B25 #53C15 #53C42 #53D12 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2007.13449

Abstract

H-umbilicity was introduced as an analogue of total umbilicity for Lagrangian submanifolds since, in some relevant cases, totally umbilical Lagrangian submanifolds are automatically totally geodesic. In this paper, we show that in the homogeneous nearly Kähler \mathbbS³×\mathbbS³, also H-umbilical Lagrangian submanifolds are automatically totally geodesic.

Related

• Lagrangian H-umbilical submanifolds in quaternion Euclidean spaces
• Lagrangian Submanifolds with Constant Angle Functions of the nearly Kähler \mathbbS³×\mathbbS³
• Lagrangian submanifolds of the nearly Kähler \mathbbS³ × \mathbbS³ from minimal surfaces in \mathbbS³
• Lagrangian submanifolds of the nearly Kähler full flag manifold F_1,2(ℂ³)
• Lagrangian submanifolds in the nearly kaehler s³ × s³