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October 13, 2025Open Access

Mean curvature flow for principal orbits of Hermann actions on rank two symmetric spaces

Key Points

Mean curvature flows illustrate behavior in rank two symmetric spaces, affecting principal orbits.
Velocity vector fields were calculated on the orbit space, defined as a 2-simplex under Hermann actions.
Using Mathematicae, we identified the position of the minimal principal orbit within the orbit space.
The results may deepen understanding of geometric flow behavior in symmetric spaces under specific actions.

Abstract

In this paper, we illustrate the behaviour of the mean curvature flows starting from principal orbits of any commuting Hermann action of cohomogeneity two on irreducible rank two Riemannian symmetric spaces of compact type by using Mathematicae. In more detail, we illustrate the velocity vector fields of the curves (determined by the flows) on the orbit space (which is a 2-simplex) of the Hermann action by using Mathematcae. Also, we calculate the position of the point of the orbit space corresponding to the only minimal principal orbit of the Hermann action by using Mathematicae.

Mean curvature flow for principal orbits of Hermann actions on rank two symmetric spaces

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Abstract

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