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arXiv · 2007.13449

$H$-umbilical Lagrangian submanifolds of the nearly K\"ahler $\mathbb{S}^3\times\mathbb{S}^3$

Miroslava Antić·Marilena Moruz·Joeri Van der Veken
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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 K\"ahler $\mathbb{S}^3\times\mathbb{S}^3$, also $H$-umbilical Lagrangian submanifolds are automatically totally geodesic.

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Miroslava Antić, Marilena Moruz, Joeri Van der Veken. 2020-07-27. $H$-umbilical Lagrangian submanifolds of the nearly K\"ahler $\mathbb{S}^3\times\mathbb{S}^3$. https://arxiv.org/abs/2007.13449

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