<em>H</em>-Umbilical Lagrangian Submanifolds of the Nearly Kähler \( {\mathbb{S}^3\times\mathbb{S}^3} \)
Miroslava Antić, Marilena Moruz, Joeri Van der Veken
Abstract
<i>H</i>-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 <inline-formula><math display="inline"><semantics><mrow><msup><mi mathvariant="double-struck">S</mi><mn>3</mn></msup><mo>×</mo><msup><mi mathvariant="double-struck">S</mi><mn>3</mn></msup></mrow></semantics></math></inline-formula>, also <i>H</i>-umbilical Lagrangian submanifolds are automatically totally geodesic.
Topics & Concepts
LagrangianGeodesicHomogeneousTotally geodesicMathematicsPure mathematicsMathematical analysisPhysicsMathematical physicsCombinatoricsGeometric Analysis and Curvature FlowsGeometry and complex manifoldsAdvanced Differential Geometry Research