On proper complex equifocal submanifolds
Naoyuki Koike
TL;DR
This paper investigates the properties of proper complex equifocal submanifolds, establishing conditions under which they are principal orbits of Hermann type actions and when they are curvature-adapted.
Contribution
It provides new criteria linking proper complex equifocal submanifolds with Hermann type actions and curvature-adaptedness.
Findings
Curvature-adapted proper complex equifocal submanifolds are principal orbits of Hermann type actions under certain conditions.
Proper complex equifocal submanifolds are curvature-adapted under specific conditions.
Abstract
First we show that a curvature-adapted proper complex equifocal submanifold is a principal orbit of a Hermann type action under certain condition. Next we show that a proper complex equifocal submanifold is curvature-adapted under certain condition.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Advanced Differential Geometry Research